Types of number — Paper 2 · IGCSE Mathematics - International 0607

3 x = 5 Write down the two possible values of x. x = … or x = … [1]

1 marks

Mark scheme: 3 – 5 and 5 1

This question in 0607/23 May/June 2017

2 Written as the product of their prime factors, 7056 = 2 4 # 3 2 # 7 2 and 8232 = 2 3 # 3 # 7 3 . Giving your answers as the product of prime factors, find (a) the highest common factor (HCF) of 7056 and 8232, … [1] (b) the lowest common multiple (LCM) of 7056 and 8232, … [1] (c) 7056. … [1]

3 marks

Mark scheme: 2(a) 23 × 3[1] × 72 isw 1 2(b) 24 × 32 × 73 isw 1 2(c) 22 × 3[1] × 7[1] isw 1

This question in 0607/21 Oct/Nov 2017

1 27 39 49 51 53 55 58 From this list write down the prime number. … [1]

1 marks

Mark scheme: Question Answer Marks Partial Marks 1 53 1

This question in 0607/23 Oct/Nov 2017

2 Find the highest common factor (HCF) of 96 and 60. … [1]

1 marks

Mark scheme: 2 12 1

This question in 0607/23 May/June 2018

6 (a) Find a fraction, n, that satisfies this inequality. 5 6 1 n 1 7 7 n = … [1] (b) Write down an irrational number, m, that satisfies this inequality. 4 1 m 1 7 m = … [1]

2 marks

Mark scheme: 6(a) Any fraction in range 1 11 3 4 e.g. , , 14 4 5 6(b) Any irrational number in range 1 e.g. a where 16 < (integer a) < 49, 2π a ≠ 25 or 36

This question in 0607/23 May/June 2018

8 Written as the product of its prime factors, 540 = 2 2 # 3 3 # 5 . (a) Write 360 as a product of its prime factors. … [2] (b) Find the highest common factor (HCF) of 540 and 360. … [1] (c) 540n is a cube number. Find the smallest possible value of n. … [1]

4 marks

Mark scheme: 8(a) 23 × 32 × 5 must be in index form 2 M1 for three steps in a ‘factor tree’ or ‘factor ladder’ or B1 for 2p × 3q × 5 8(b) 180 or 22 × 32 × 5 1 8(c) 50 or 2 × 52 1

This question in 0607/22 Oct/Nov 2020

8 Find the value of - 4 + 4 . … [1]

1 marks

Mark scheme: 8 8 1

This question in 0607/23 May/June 2021

3 (a) A number is greater than 1. The number is also both a square number and a cube number. Write down a possible value of this number. … [1] (b) Write down a prime number between 90 and 100. … [1]

2 marks

Mark scheme: 3(a) 64 1 3(b) 97 only 1

This question in 0607/22 Oct/Nov 2021

3 21 24 25 27 29 39 48 From the list of numbers, write down (a) the prime number, … [1] (b) the cube number. … [1]

2 marks

Mark scheme: 3(a) 29 only 1 3(b) 27 only 1

This question in 0607/21 May/June 2022

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

2 marks

Mark scheme: 9 2 × 3 × 3 × 5 or 2 × 32 × 5 final answer 2 M1 for 2, 3 and 5 seen as factors

This question in 0607/21 May/June 2022

4 (a) Express 175 as the product of its prime factors. … [2] (b) Kurt has two timers. One is set to ring every 175 minutes. The other is set to ring every 70 minutes. Both timers ring together at 09 15. Find the time when the timers next ring together. … [3]

5 marks

Mark scheme: 4(a) 5 × 5 × 7 or 52 × 7 2 B1 for 5 and 7 identified as factors 4(b) 15 05 3 B2 for [LCM=] 350 or B1 for 2 × 5 × 7 or 10 25, 11 35, 12 45... or 70, 140, 210, 280, 350

This question in 0607/23 May/June 2022

1 71 73 75 77 79 81 87 From this list of numbers write down (a) a prime number … [1] (b) a square number. … [1]

2 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 71 or 73 or 79 1 1(b) 81 1

This question in 0607/22 Feb/March 2023

1 Write down (a) a square number between 101 and 150 … [1] 2 3 (b) a fraction between and 3 4 … [1] (c) an irrational number between 6 and 7. … [1]

3 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 121 or 144 1 1(b) Any correct fraction 1 1(c) Any correct irrational number 1

This question in 0607/22 May/June 2023

1 29 31 41 49 51 59 From this list, write down all the numbers that are prime numbers. … [2]

2 marks

Mark scheme: Question Answer Marks Partial Marks 1 29 31 41 59 2 B1 for at least two correct

This question in 0607/23 May/June 2023

4 (a) Write 1.8796 correct to 4 significant figures. … [1] 4 (b) Work out 5 . ` j … [1] (c) x is an integer and x G 1. Write down the values of x. … [1] (d) Find the highest common factor (HCF) of 24 and 42. … [1]

4 marks

Mark scheme: 4(a) 1.880 cao 1 4(b) 25 1 4(c) –1, 0, 1 1 4(d) 6 1

This question in 0607/21 Oct/Nov 2023

7 Write down an irrational number between 3 and 4. … [1]

1 marks

Mark scheme: 7 an irrational number between 3 and 4 1 e.g. π, √10 etc.

This question in 0607/22 Oct/Nov 2023

7 a, b and c are prime numbers. V = a 2 b 4 c 3 W = a 5 b 3 c Find the lowest common multiple (LCM) of V and W in terms of a, b and c. … [2]

2 marks

Mark scheme: 7 a5b4c3 Final answer 2 B1 for a5b4ck or a5bkc3 or akb4c3 or for any common multiple

This question in 0607/23 May/June 2024

1 This is a list of numbers. 2 3.142 125 125 81 7 3 From this list write down (a) a cube number … [1] (b) an irrational number. … [1]

2 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 125 1 1(b) 1 125

This question in 0607/21 May/June 2025

12 P = 2 3 # 3 a # 5 b # 7 Q = 2 # 3 5 # 7c The highest common factor (HCF) of P and Q is 2 # 3 4 # 7 . The lowest common multiple (LCM) of P and Q is 2 3 # 3 5 # 5 2 # 7 . Find the values of a, b and c. a = … b = … c = … [3]

3 marks

Mark scheme: 12 a = 4 3 B1 for each b = 2 c = 1

This question in 0607/21 May/June 2025