Types of number — Paper 2 · IGCSE Mathematics 0580

1 A pattern of numbers is shown below. For Examiner's 1 Use 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 1 6 x 20 x 6 1 Write down the value of x. Answer [1]

1 marks

Mark scheme: 1 15 1

This question in 0580/21 Oct/Nov 2004

22 65 3 From the list of numbers , π , 14 , 16 , 27.4, write down 7 13 (a) one integer, Answer(a) [1] (b) one irrational number. Answer(b) [1]

2 marks

Mark scheme: 3 (a) √16 or 65/13 1 Allow 4 or 5 (b) π or √14 1 Not 22/7

This question in 0580/21 Oct/Nov 2004

2 Write down the next two prime numbers after 43. Answer and [2]

2 marks

Mark scheme: 2 47, 53 2 B1, B1 independent

This question in 0580/21 Oct/Nov 2009

3 p is the largest prime number between 50 and 100. q is the smallest prime number between 50 and 100. Calculate the value of p – q. Answer [2]

2 marks

Mark scheme: 3 44 2 M1 97 or 53 seen

This question in 0580/21 May/June 2010

11 NOT TO SCALE O Q C 6 cm 4 cm P T Two circles, centres O and C, of radius 6 cm and 4 cm respectively, touch at Q. PT is a tangent to both circles. (a) Write down the distance OC. Answer(a) OC = cm [1] (b) Calculate the distance PT. Answer(b) PT = cm [3]

4 marks

Mark scheme: 11 (a) 10(.0..) 1 (b) 9.80 3 M2 √((a)2 – 22) or M1 PT2 + 22 = (a)2 h

This question in 0580/22 May/June 2010

2 210 211 212 213 214 215 216 From the list of numbers, find (a) a prime number, Answer(a) [1] (b) a cube number. Answer(b) [1]

2 marks

Mark scheme: 2 (a) 211 cao 1 (b) 216 cao 1

This question in 0580/23 Oct/Nov 2011

11 The sum of the prime numbers less than 8 is equal to 17. For Examiner′s Use (a) Find the sum of the prime numbers less than 21. Answer(a) … [2] (b) The sum of the prime numbers less than x is 58. Find an integer value for x. Answer(b) x = … [2] _____________________________________________________________________________________

4 marks

Mark scheme: 11 (a) 77 2 M1 for 11,13,17,19 clearly identified, ignore numbers less than 8 with no other numbers greater than or equal to 8 besides possibly an extra 17 (b) either 18 or 19 or both 2FT M1 for 11,13,17 clearly identified, ignore numbers less than 8 with no other numbers greater than or equal to 8 besides possibly an extra 17 or for their (a) − 58

This question in 0580/23 May/June 2013

15 (a) Write 90 as a product of prime factors. Answer(a) … [2] (b) Find the lowest common multiple of 90 and 105. Answer(b) … [2] __________________________________________________________________________________________

4 marks

Mark scheme: 15 (a) 2 × 3 × 3 × 5 2 B1 for 2, 3, [3] and 5 identified as only prime factors or M1 for partial prime factorisation 6 × 3 × 5 or 2 × 9 × 5 or 3 × 3 × 10 or 2 × 3 × 15 (b) 630 2 M1 for 2 × 32 × 5 × 7 oe or for listing multiples of 90 and 105 at least up to 630

This question in 0580/22 Oct/Nov 2014

7 Work out the highest common factor (HCF) of 36 and 90. Answer … [2] __________________________________________________________________________________________

2 marks

Mark scheme: 7 18 2 M1 for 36 = 2 × 2 × 3 × 3 soi or 90 = 2 × 3 × 3 × 5 soi or listing the correct factors of 36 and 90 showing a minimum of 2, 3, 6, 9 and 18

This question in 0580/21 Oct/Nov 2015

5 11 12 13 14 15 16 From the list of numbers, write down (a) the factors of 60, Answer(a) … [1] (b) the prime numbers. Answer(b) … [1] __________________________________________________________________________________________

2 marks

Mark scheme: 5 (a) 12, 15 1 (b) 11, 13 1

This question in 0580/23 Oct/Nov 2015

13 (a) Write 2016 as the product of prime factors. … [3] (b) Write 2016 in standard form. … [1]

4 marks

Mark scheme: 13 (a) 2 5 × 32 × 7 oe final answer 3 B2 for product of two of 2 5 , 3 2 , 7 or B1 for 2, 3 and 7 seen or M1 for 2 × 1008 or 3 × 672 or 7 × 288 soi (b) 2.016 × 10 3 1 8 7 8 k k 7

This question in 0580/22 Feb/March 2016

6 Find the lowest common multiple (LCM) of 36 and 48. … [2]

2 marks

Mark scheme: 6 144 2 M1 for finding a correct product of prime factors or correctly listing a minimum of 3 multiples of 36 and 48 or for answer 24 × 32 oe or 144k

This question in 0580/21 May/June 2016

10 Find the highest common factor (HCF) of 56 and 70. … [2]

2 marks

Mark scheme: 10 14 2 M1 for 56 = 2×2×2×7 soi or 70 = 2×5×7 soi or 2×7 as final answer

This question in 0580/23 May/June 2016

3 Find the lowest common multiple (LCM) of 20 and 24. … [2]

2 marks

Mark scheme: 3 120 2 M1 for finding a correct product of prime factors or correctly listing a minimum of 3 multiples of 20 and 24 or for answer 23 × 3 × 5 oe or 120k where k is an integer > 1

This question in 0580/23 May/June 2017

16 (a) Solve the inequality. x + 13 H 3x + 7 … [2] (b) List the positive integers that satisfy the inequality in part (a). … [1]

3 marks

Mark scheme: 16(a) x ⩽ 3 final answer 2 M1 for 13 − 7 ⩾ 3x − x oe 16(b) 1, 2, 3 1FT correct answer or FT their answer to (a)

This question in 0580/23 May/June 2017

112 5 -7 343 -11 0.4 2.5 3 From this list of numbers, write down (a) a cube number, … [1] (b) the smallest number, … [1] (c) a natural number. … [1]

3 marks

Mark scheme: 12(a) 343 1 12(b) –11 1 12(c) 343 1

This question in 0580/21 Oct/Nov 2017

4 (a) 1 and 12 are factors of 12. Write down all the other factors of 12. … [1] (b) Write down the multiples of 9 between 20 and 40. … [1]

2 marks

Mark scheme: 4(a) 2, 3, 4, 6 1 4(b) 27, 36 cao 1

This question in 0580/22 Oct/Nov 2017

1 Write down a prime number between 20 and 30. … [1]

1 marks

Mark scheme: Question Answer Marks Partial Marks 1 23 or 29 1

This question in 0580/21 May/June 2018

5 22 17 25 41 39 4 Work out the difference between the two prime numbers in the list above. … [2]

2 marks

Mark scheme: 5 24 2 B1 for 17 or 41 identified

This question in 0580/22 May/June 2018

4 Complete the list of factors of 36. 1, 2, … , 36 [2]

2 marks

Mark scheme: 4 3, 4, 6, 9, 12, 18 2 B1 for list with one or two errors or omissions or for a complete list of products

This question in 0580/23 May/June 2018

23 (a) Write 56 as a product of its prime factors. … [2] (b) Find the lowest common multiple (LCM) of 56 and 42. … [2]

4 marks

Mark scheme: 23(a) 23 × 7 or 2 × 2 × 2 × 7 2 B1 for identifying 2 and 7 as the only prime factors 23(b) 168 2 B1 for 168k or 2 × 2 × 2 × 3 × 7 oe or for listing multiples of each up to 168

This question in 0580/22 Oct/Nov 2018

6 (a) Write the number five million, two hundred and seven in figures. … [1] (b) Write 0.008 13 in standard form. … [1]

2 marks

Mark scheme: 6(a) 5 000 207 1 6(b) 8.13 × 10−3 1

This question in 0580/23 Oct/Nov 2018

12 27 28 29 30 31 32 33 From the list of numbers, write down (a) a multiple of 7, … [1] (b) a cube number, … [1] (c) a prime number. … [1]

3 marks

Mark scheme: 12(a) 28 1 12(b) 27 1 12(c) 29 or 31 1

This question in 0580/21 May/June 2019

1 Write down a prime number between 50 and 60. … [1]

1 marks

Mark scheme: Question Answer Marks Partial Marks 1 53 or 59 1

This question in 0580/22 May/June 2019

9 Find the highest common factor (HCF) of 90 and 48. … [2]

2 marks

Mark scheme: 9 6 2 M1 for 2 × 32 × 5 or 24 × 3 or for 2 × 3 as final answer or B1 for 2 or 3 as final answer

This question in 0580/22 May/June 2019

7 Here is a list of numbers. 21 23 13 31 121 51 0.7 From this list, write down (a) a prime number, … [1] (b) an irrational number. … [1]

2 marks

Mark scheme: 7(a) 31 or 121 1 7(b) 13 1

This question in 0580/23 May/June 2019

4 Write 15 060 (a) in words, … [1] (b) in standard form. … [1]

2 marks

Mark scheme: 4(a) Fifteen thousand [and] sixty 1 4(b) 1.506[0] × 104 1

This question in 0580/21 Oct/Nov 2019

3 Here is a list of numbers. 87 77 57 47 27 From this list, write down (a) a cube number, … [1] (b) a prime number. … [1]

2 marks

Mark scheme: 3(a) 27 1 3(b) 47 1

This question in 0580/23 Oct/Nov 2019

4 Find the highest common factor (HCF) of 84 and 105. … [2]

2 marks

Mark scheme: 4 21 2 M1 for [84 =] 2 × 2 × 3 × 7 or [105 =] 3 × 5 × 7 or 3 × 7 as final answer or B1 for 3 or 7 as final answer

This question in 0580/23 Oct/Nov 2019

1 3.56 5 196 8 7 12 From the list, write down a number that is (a) a multiple of 3, … [1] (b) a cube number, … [1] (c) a prime number, … [1] (d) an irrational number. … [1]

4 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 12 1 1(b) 8 1 1(c) 5 1 1(d) 7 1

This question in 0580/22 Feb/March 2020

2 Find the highest odd number that is a factor of 60 and a factor of 90. … [1]

1 marks

Mark scheme: 2 15 1

This question in 0580/21 May/June 2020

7 234 = 2 # 3 2 # 13 1872 = 2 4 # 3 2 # 13 234 # 1872 = 438048 Use this information to write 438 048 as a product of its prime factors. … [1]

1 marks

Mark scheme: 7 25 × 34 × 132 1

This question in 0580/21 May/June 2020

4 Write down (a) a square number greater than 10, … [1] (b) an irrational number. … [1]

2 marks

Mark scheme: 4(a) Any square number greater than 10 1 4(b) Any irrational number 1

This question in 0580/22 May/June 2020

1 32 33 34 35 36 37 38 39 From this list of numbers, write down (a) a multiple of 8, … [1] (b) a square number, … [1] (c) a prime number. … [1]

3 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 32 1 1(b) 36 1 1(c) 37 1

This question in 0580/23 May/June 2020

8 (a) 1, 2, 3, 5 and 7 are all common factors of two numbers. Write down the digit that the two numbers must end in. … [1] (b) Write 84 as a product of its prime factors. … [2]

3 marks

Mark scheme: 8(a) 0 1 8(b) 22 × 3 × 7 or 2 × 2 × 3 × 7 2 B1 for 2, 2, 3, 7

This question in 0580/21 Oct/Nov 2020

1 Write two hundred thousand and seventeen in figures. … [1]

1 marks

Mark scheme: Question Answer Marks Partial Marks 1 200 017 1

This question in 0580/22 Oct/Nov 2020

11 Find the highest common factor (HCF) of 36 and 84. … [2]

2 marks

Mark scheme: 11 12 2 M1 for 22 × 32 and 22×3×7 or for 2 × 2 × 3 final answer or B1 for 2, 3, 4 or 6 as final answer

This question in 0580/22 Feb/March 2021

4 Write down an expression for the range of k consecutive integers. … [1]

1 marks

Mark scheme: 4 k – 1 1

This question in 0580/22 May/June 2021

7 (a) Complete these statements. The reciprocal of 0.2 is … A prime number between 90 and 100 is … [2] (b) 7 0.6 7 8 9 5 From this list, write down an irrational number. … [1]

3 marks

Mark scheme: 7(a) 5 2 B1 for each 97 7(b) 7 1

This question in 0580/22 May/June 2021

7 12 18 29 49 91 125 From the list of numbers, write down (a) a cube number, … [1] (b) a prime number. … [1]

2 marks

Mark scheme: 7(a) 125 1 7(b) 29 1

This question in 0580/23 May/June 2021

1 P is a prime number where 60 1 P 1 80 . P is 2 less than a square number. Find the value of P. P = … [2]

2 marks

Mark scheme: Question Answer Marks Partial Marks 1 79 2 B1 for 64 or 81 seen or for answer 61, 62, 67, 71 or 73

This question in 0580/21 Oct/Nov 2021

3 11 13 15 17 19 From this list, write down the number that is both a prime number and a factor of 195. … [1]

1 marks

Mark scheme: 3 13 1

This question in 0580/23 Oct/Nov 2021

1 Write down a prime number between 30 and 40. … [1]

1 marks

Mark scheme: Question Answer Marks Partial Marks 1 31 or 37 1

This question in 0580/21 May/June 2022

6 Write 180 as a product of its prime factors. … [2]

2 marks

Mark scheme: 6 2 × 2 × 3 × 3 × 5 oe 2 B1 for 2, 2, 3, 3, 5 or M1 for correct factor tree/diagram/table.

This question in 0580/21 May/June 2022

12 f is a common factor of 14 and 28. m is a common multiple of 10 and 25. p is a prime number. f Work out the largest possible value of . mp … [4]

4 marks

Mark scheme: 12 0.14 oe nfww 4 14 M3 for with at least 2 out of 3 50  2 values correct and for the one incorrect value: f must be 1, 2 or 7 m must be a multiple of 50 p must be prime OR B1 for f = 14 B1 for m = 50 B1 for p = 2 If 0 scored SC1 for a correct multiple for m, factor for f or prime for p

This question in 0580/23 May/June 2022

1 Write down a common multiple of 18 and 24. … [1]

1 marks

Mark scheme: Question Answer Marks Partial Marks 1 Any multiple of 72 1

This question in 0580/21 Oct/Nov 2022

2 120 121 149 164 216 From this list, write down (a) a square number … [1] (b) a cube number. … [1]

2 marks

Mark scheme: 2(a) 121 1 2(b) 216 1

This question in 0580/23 Oct/Nov 2022

7 Find the lowest common multiple (LCM) of 36 and 60. … [2]

2 marks

Mark scheme: 7 180 2 M1 for answer 2  2  3  3  5 or better or for answer 180k or two correct factor trees, tables or Venn diagram or better or a list of multiples of both 36 and 60 with at least 3 correct of each

This question in 0580/23 Oct/Nov 2022

1 12 15 27 29 91 93 From the list of numbers, write down (a) a cube number … [1] (b) a prime number. … [1]

2 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 27 1 1(b) 29 1

This question in 0580/22 Feb/March 2023

2 There are two prime numbers in this list. 27 47 57 61 75 93 Work out the sum of these two prime numbers. … [2]

2 marks

Mark scheme: 2 108 2 B1 for 47 or 61 identified

This question in 0580/22 May/June 2023

9 Find the highest common factor (HCF) of 140 and 126. … [2]

2 marks

Mark scheme: 9 14 2 B1 for answer 2 or 7 or M1 for 2 × 7 as final answer or [140 =] 2 × 2 × 5 × 7 and [126 =] 2 × 3 × 3 × 7 or 2 correct factor trees or tables

This question in 0580/21 Oct/Nov 2023

6 (a) Explain why 111 is not a prime number. … [1] (b) Find a prime number between 110 and 120. … [1]

2 marks

Mark scheme: 6(a) Multiple of 3 or multiple of 37 1 6(b) 113 1

This question in 0580/22 Oct/Nov 2023

9 Write 90 as a product of its prime factors. … [2]

2 marks

Mark scheme: 9 2 × 3 × 3 × 5 or 2  32  5 2 B1 for 2, 3, 3, 5 or M1 for correct factor tree/diagram/list/table.

This question in 0580/22 Oct/Nov 2023

2 61 63 64 66 68 69 From this list, write down (a) a cube number … [1] (b) a prime number. … [1]

2 marks

Mark scheme: 2(a) 64 1 2(b) 61 1

This question in 0580/23 Oct/Nov 2023

8 Find the highest common factor (HCF) of 48 and 80. … [2]

2 marks

Mark scheme: 8 16 2 B1 for answer 2 or 4 or 8 or M1 for 2  2  2  2 oe as final answer or [48 =] 2  2  2  2  3 and [80 =] 2  2  2  2  5 or for 2 correct factor trees or tables

This question in 0580/23 Oct/Nov 2023

4 Find the greatest odd number that is a factor of 140 and a factor of 210. … [2]

2 marks

Mark scheme: 4 35 2 B1 for answer 5, 7 or 70 or M1 for 2 × 2 × 5 × 7 and 2 × 3 × 5 × 7 or two correct factor trees or tables or 5 × 7 × k seen

This question in 0580/21 May/June 2024

1 Write the number two million two thousand and two in figures. … [1]

1 marks

Mark scheme: Question Answer Marks Partial Marks 1 2 002 002 1

This question in 0580/23 May/June 2024

3 1 0.25 3.142 3 - 3 24 - .04 1.2 - 4 Complete each statement with a number from the list. … is a natural number. … is an irrational number. … is the reciprocal of 4. [3]

3 marks

Mark scheme: 3 24 3 B1 for each 3 0.25

This question in 0580/22 Oct/Nov 2024

8 Find the highest common factor (HCF) of 36 and 54. … [2]

2 marks

Mark scheme: 8 18 2 B1 for answer 2, 3, 6 or 9 or M1 for answer 2 × 32 oe or for 2 × 2 × 3 × 3 and 2 × 3 × 3 × 3 or 2 correct factor trees or tables

This question in 0580/22 May/June 2025

8 (a) Write 42 as a product of its prime factors. … [2] (b) Find the highest common factor (HCF) of 84 and 70. … [2]

4 marks

Mark scheme: 8(a) 2 × 3 × 7 2 B1 for 2, 3, 7 or M1 for correct factor tree/diagram/table 8(b) 14 2 B1 for answer 2 or 7 or M1 for 2 × 7 as final answer or 84 = 2 × 2 × 3 × 7 and 70 = 2 × 5 × 7 or 2 correct factor trees or tables

This question in 0580/23 May/June 2025

2 Find all the common factors of 8 and 12. … [1]

1 marks

Mark scheme: 2 1, 2, 4 1

This question in 0580/22 Oct/Nov 2025

2 Find the largest odd number that is a common factor of 90 and 120. … [1]

1 marks

Mark scheme: 2 15 1

This question in 0580/23 Oct/Nov 2025

3 The diagram shows a net for a dice. The dice has six faces numbered 1 to 6. The sum of each pair of opposite faces on the dice is 7. Write the missing numbers on the net. … 1 4 5 … … [1]

1 marks

Mark scheme: 3 1 2 1 4 5 6 3

This question in 0580/23 Oct/Nov 2025

7 (a) The sum of all the prime numbers less than 10 is equal to 17. Find the sum of all the prime numbers less than 16. … [2] (b) x is an integer. The sum of the prime numbers greater than 6 and less than x is equal to 18. Find a possible value for x. x = … [1]

3 marks

Mark scheme: 7(a) 41 2 B1 for 11 or 13 seen with no more than one incorrect value 7(b) 12 or 13 1

This question in 0580/23 Oct/Nov 2025