Practice Factors and multiples
A divisor divides a whole number without a remainder; a multiple is a whole-number product of that number.
Both help with grouping quantities and finding common denominators.
Exercises with solutions
A divisor fits into a number without a remainder. A multiple is what you get when you multiply a number by 1, 2, 3 … For the greatest common divisor (gcd) you look for the largest number dividing both, for the least common multiple (lcm) the smallest number appearing in both lists.
Exercise 1
List all divisors of 12.
Show solution and working
1, 2, 3, 4, 6, 12
Check in turn: 12 ÷ 1, 12 ÷ 2, 12 ÷ 3, 12 ÷ 4, 12 ÷ 6 and 12 ÷ 12 all leave no remainder.
Exercise 2
Is 7 a divisor of 91?
Show solution and working
Yes, because 91 = 7 · 13
Divide 91 by 7: 91 ÷ 7 = 13 with remainder 0. So 7 is a divisor of 91.
Exercise 3
Find the gcd of 18 and 24.
Show solution and working
6
Divisors of 18: 1, 2, 3, 6, 9, 18. Divisors of 24: 1, 2, 3, 4, 6, 8, 12, 24. The largest number in both lists is 6.
Exercise 4
Find the lcm of 4 and 6.
Show solution and working
12
Multiples of 4: 4, 8, 12, 16 … Multiples of 6: 6, 12, 18 … The smallest shared number is 12.
Common mistake
Confusing divisors and multiples. Divisors are at most as large as the number itself (4 divides 12), multiples are at least as large (12 is a multiple of 4).
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