11+ Number Properties Online Tests
Number properties is the study of how whole numbers behave: which numbers divide into which, which have no factors at all, and which patterns they form. The 11+ uses it both directly and as the hidden machinery inside fraction and ratio questions.
Factors, multiples, primes and square numbers are the core. Grammar school papers frequently ask for the highest common factor or lowest common multiple of two numbers, and almost always assume the primes up to 50 are known on sight rather than worked out.
21 free Number Properties tests
Timed and marked instantly, with an explanation for every question. No sign-up needed.
- Number Properties: Easy Test 1 Easy 15 questions · 15 min
- Number Properties: Easy Test 2 Easy 15 questions · 15 min
- Number Properties: Easy Test 3 Easy 15 questions · 15 min
- Number Properties: Easy Test 4 Easy 15 questions · 15 min
- Number Properties: Easy Test 5 Easy 15 questions · 15 min
- Number Properties: Medium Test 1 Medium 15 questions · 15 min
- Number Properties: Medium Test 2 Medium 15 questions · 15 min
- Number Properties: Medium Test 3 Medium 15 questions · 15 min
- Number Properties: Medium Test 4 Medium 15 questions · 15 min
- Number Properties: Medium Test 5 Medium 15 questions · 15 min
- Number Properties: Medium Test 6 Medium 15 questions · 15 min
- Number Properties: Medium Test 7 Medium 15 questions · 15 min
- Number Properties: Medium Test 8 Medium 15 questions · 15 min
- Number Properties: Hard Test 1 Hard 15 questions · 15 min
- Number Properties: Hard Test 2 Hard 15 questions · 15 min
- Number Properties: Hard Test 3 Hard 15 questions · 15 min
- Number Properties: Hard Test 4 Hard 15 questions · 15 min
- Number Properties: Hard Test 5 Hard 15 questions · 15 min
- Number Properties: Hard Test 6 Hard 15 questions · 15 min
- Number Properties: Hard Test 7 Hard 15 questions · 15 min
- Number Properties: Hard Test 8 Hard 15 questions · 15 min
What these Number Properties tests cover
- Factors, factor pairs and finding all factors of a number
- Multiples and common multiples
- Prime numbers and prime factorisation
- Highest common factor and lowest common multiple
- Square numbers, cube numbers and square roots
- Divisibility rules for 2, 3, 4, 5, 6, 9 and 10
Number Properties: tips that earn marks
- Learn the primes up to 50 by heart: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47. Remember that 1 is not prime and 2 is the only even prime.
- Find factors in pairs and work upwards - 1 and 24, 2 and 12, 3 and 8, 4 and 6 - and you will not miss any.
- A number is divisible by 3 if its digits add to a multiple of 3, and by 9 if they add to a multiple of 9. This turns a long division into a two-second check.
- Know the square numbers to 15 x 15; they appear in area, algebra and sequence questions as well as here.
Questions parents ask about Number Properties
Is 1 a prime number?
No. A prime number has exactly two different factors, itself and 1. Since 1 has only one factor it is not prime, and this is a favourite 11+ trick question.
Do children need prime factorisation for the 11+?
For most boards it is useful rather than essential, but it makes highest common factor and lowest common multiple questions much faster and more reliable.
What is the difference between a factor and a multiple?
A factor divides into the number; a multiple is the number multiplied up. 4 is a factor of 12, and 24 is a multiple of 12. Children mix these two words up constantly, so it is worth over-practising.