Understand the rule first
Factors divide exactly; multiples appear in a multiplication sequence. Prime numbers have exactly two positive factors: 1 and themselves.
Factors, multiples & number properties 11+ practice
Use factors, multiples, primes and divisibility to reason efficiently.
Find the highest common factor of 36 and 54.
- Factors of 36 include 1, 2, 3, 4, 6, 9, 12, 18 and 36.
- Factors of 54 include 1, 2, 3, 6, 9, 18, 27 and 54.
- The greatest shared factor is 18.
A common misconception
Confusing a factor of a number with a multiple of that number.
Reusable method: List systematically so no factor or multiple is missed.Question 1 of 10 MathscoreWhich number is prime?
- A21
- B27
- C29
- D39
Need a hint?
Test divisibility by primes no greater than the square root.
Show worked answer
Answer C: 29
29 has no positive factors other than 1 and 29.
Quick method: List systematically so no factor or multiple is missed.
Question 2 of 10 MathscoreWhat is the greatest common factor of 24 and 40?
- A4
- B5
- C10
- D8
Need a hint?
List factor pairs for both numbers.
Show worked answer
Answer D: 8
The common factors are 1, 2, 4 and 8; the greatest is 8.
Quick method: List systematically so no factor or multiple is missed.
Question 3 of 10 MathscoreWhich number is divisible by both 3 and 5?
- A120
- B123
- C125
- D128
Need a hint?
It must end in 0 or 5 and have digits summing to a multiple of 3.
Show worked answer
Answer A: 120
120 ends in 0 and 1 + 2 + 0 = 3, so it is divisible by both.
Quick method: List systematically so no factor or multiple is missed.
Question 4 of 10 Mathsexam-styleTwo bells ring every 6 minutes and every 8 minutes. If they ring together now, when will they next ring together?
- A12 minutes
- B24 minutes
- C48 minutes
- D14 minutes
Need a hint?
Find the lowest common multiple of 6 and 8.
Show worked answer
Answer B: 24 minutes
The lowest common multiple of 6 and 8 is 24.
Quick method: List systematically so no factor or multiple is missed.
Question 5 of 10 Mathsexam-styleA number is a factor of 72 and a multiple of 9. Which could it be?
- A7
- B12
- C18
- D45
Need a hint?
Check which option divides 72 exactly and also lies in the 9 times table.
Show worked answer
Answer C: 18
18 is 9 × 2 and 72 ÷ 18 = 4.
Quick method: List systematically so no factor or multiple is missed.
Question 6 of 10 MathscoreWhat is the highest common factor of 48 and 72?
- A24
- B12
- C18
- D36
Need a hint?
List the factors or use prime factors.
Show worked answer
Answer A: 24
48 = 2⁴ × 3 and 72 = 2³ × 3². Their shared factors give 2³ × 3 = 24.
Quick method: List systematically so no factor or multiple is missed.
Question 7 of 10 MathscoreWhat is the lowest common multiple of 12 and 18?
- A24
- B36
- C54
- D72
Need a hint?
List multiples until the first match.
Show worked answer
Answer B: 36
Multiples of 12 are 12, 24, 36… and multiples of 18 are 18, 36… The first common multiple is 36.
Quick method: List systematically so no factor or multiple is missed.
Question 8 of 10 MathscoreWhich is the prime factorisation of 84?
- A2 × 3 × 14
- B2² × 21
- C2² × 3 × 7
- D2 × 3² × 7
Need a hint?
Keep dividing until every factor is prime.
Show worked answer
Answer C: 2² × 3 × 7
84 = 2 × 42 = 2 × 2 × 21 = 2² × 3 × 7.
Quick method: List systematically so no factor or multiple is missed.
Question 9 of 10 MathsexamWhich number between 70 and 100 is divisible by both 6 and 8?
- A78
- B84
- C90
- D96
Need a hint?
A number divisible by both must be a multiple of their lowest common multiple.
Show worked answer
Answer D: 96
The lowest common multiple of 6 and 8 is 24. The multiple of 24 between 70 and 100 is 96.
Quick method: List systematically so no factor or multiple is missed.
Question 10 of 10 MathsstretchWhat is the smallest whole number greater than 3 that leaves remainder 3 when divided by both 5 and 7?
- A38
- B33
- C35
- D73
Need a hint?
Subtract the remainder: the result must be divisible by both 5 and 7.
Show worked answer
Answer A: 38
The number minus 3 must be the lowest common multiple of 5 and 7, which is 35. Therefore the number is 35 + 3 = 38.
Quick method: List systematically so no factor or multiple is missed.