Practice Divisibility rules
Divisibility rules use digits or digit sums to check whether a whole number can be divided without a remainder.
They make factorising and simplifying fractions faster.
Exercises with solutions
Divisibility rules let you check without dividing. 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 digit sum is divisible by 3, and by 9 if its digit sum is divisible by 9.
Exercise 1
Is 4,236 divisible by 2?
Show solution and working
Yes
The last digit is 6, which is even.
Exercise 2
Is 4,236 divisible by 3?
Show solution and working
Yes
The digit sum is 4 + 2 + 3 + 6 = 15, and 15 is divisible by 3.
Exercise 3
Is 1,234 divisible by 9?
Show solution and working
No
The digit sum is 1 + 2 + 3 + 4 = 10, and 10 is not divisible by 9.
Exercise 4
Is 7,245 divisible by 5?
Show solution and working
Yes
The last digit is 5, so the number ends in 5.
Common mistake
The rule for 3 does not automatically give the rule for 9: the digit sum 15 is divisible by 3 but not by 9. Always check the digit sum itself for 9.
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