Number
Factors and multiples
Find factors and multiples, use divisibility tests, and tell a prime number from a composite one.
A factor of a number divides into it exactly, leaving nothing over. A multiple of a number is what you get when you multiply it by a whole number, so the multiples of 7 are simply the seven times table carried on for ever. Factors of a number are never bigger than it; its multiples, from the number itself onwards, are never smaller.
Prime and composite
Every number above 1 has at least two factors, 1 and itself. A prime number has exactly those two and no others. A composite number has more. The number 1 is neither: it has only one factor, so it fails the test for prime, and it has no extra factors, so it fails the test for composite.
Three divisibility tests worth memorising
A number is divisible by 2 if its last digit is even. By 5 if it ends in 0 or 5. By 3 if its digits add up to a multiple of 3, and by 9 if its digits add up to a multiple of 9 — so 4653 is divisible by 9, because 4 + 6 + 5 + 3 = 18.
Have a play
Every mark on this line is a multiple of 3. Move along them and see how many you already know from the 3 times table.
Tap anywhere on the line.
Worked example
Find every factor of 36.
Start at 1: 1 × 36 = 36. That is a pair of factors.
Factors always arrive in pairs, so finding one hands you another.
Try it together
Let us decide whether 91 is prime.
It is odd, it does not end in 0 or 5, and its digits add up to 10, so 2, 3, 5 and 9 are all ruled out. That leaves 7 as the next one worth trying.
1.What is 91 ÷ 7?
Have a go
Have a go on your own: how many factors does 20 have?
Hint: Write them in pairs: 1 and 20, then keep going.
Ready to practise?
Eight questions on what you have just read. Nothing is timed, and you can play as many times as you like.