Free Types of number questions for IGCSE Mathematics (0580), part of Number. Each question has the answer and the marking points an examiner would look for.
Generate a full Types of Number worksheet →All Number questionsA = 23 × 52 and B = 24 × 5.
Find the HCF of A and B, giving your answer as a product of prime factors.
Find the smallest positive integer k such that Ak is a square number.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 23 × 5 method M1 23 × 5 A1 | 2 |
| (b) | 2 identifies the odd powers M1 2 A1 | 2 |
This question is about the expression n2 + n + 1, where n is a positive integer.
Find all the values of n less than 50 for which n2 + n + 1 is a multiple of 7.
Prove that n2 + n + 1 is never a multiple of 5.
Find the smallest value of n for which n2 + n + 1 is a multiple of 49.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | n = 2, 4, 9, 11, 16, 18, 23, 25, 30, 32, 37, 39, 44, 46 (14 values) tests n = 1 to 7 and finds n = 2 and n = 4 M1 realises the pattern repeats every 7 (adding 7 to n adds a multiple of 7) M1 A1 for n = 2, 9, 16, … and A1 for n = 4, 11, 18, … A2 all 14 values and no extras A1 | 5 |
| (b) | last digit of n² + n + 1 is 1, 3 or 7 for every n considers n by its last digit (or n = 5k, 5k + 1, …) M1 last digits of n2 + n: 0, 2, 6, 2, 0, 0, 2, 6, 2, 0 A1 so last digit of n2 + n + 1 is 1, 3 or 7 A1 never 0 or 5, so never a multiple of 5 A1 | 4 |
| (c) | n = 18 only n = 2, 4, 9, 11, 16, 18, … need be tested (from (a)) M1 7, 21, 91, 133, 273 are not multiples of 49 M1 n = 18 (343 = 73) A1 | 3 |
Here is a list of numbers.
√36 π 3/7 √5 0.25 √9
Write down the irrational numbers.
Write down the reciprocal of 0.25.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | π, √5 π B1 √5 B1 | 2 |
| (b) | 4 4 B1 | 1 |
From the list of numbers
21 1 19 49 64 4
write down
a prime number,
a square number,
a cube number.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 19 19 B1 | 1 |
| (b) | 1 or 49 or 64 or 4 1 or 49 or 64 or 4 B1 | 1 |
| (c) | 1 or 64 1 or 64 B1 | 1 |
Write 72 as a product of its prime factors.
Find the highest common factor (HCF) of 72 and 90.
Find the lowest common multiple (LCM) of 72 and 90.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 23 × 32 23 × 32 B2 B1 for a correct factor tree or list of primes | 2 |
| (b) | 18 18 B1 | 1 |
| (c) | 360 360 B1 | 1 |
A = 32 × 5 and B = 33 × 5.
Find the HCF of A and B, giving your answer as a product of prime factors.
Find the smallest positive integer k such that Ak is a square number.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 32 × 5 method M1 32 × 5 A1 | 2 |
| (b) | 5 identifies the odd powers M1 5 A1 | 2 |
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Meet Riyaz →Original Cambridge-style practice questions written for mentorriyaz.in. These are not Cambridge past paper questions, and this site is not affiliated with or endorsed by Cambridge University Press & Assessment. Updated 2026-11-04. Paper generator · mentorriyaz.in