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Divisibility and remainders – practice for Years 6–9

Sample questions on Divisibility and remainders with the right answer and a worked solution, from easy to hard. In the Pickles Academy app a child gets new questions of the same kind every time, so they can't just learn the answers by heart.

Subject
Maths
Year
Years 6–9
Curriculum area
Number and algebra

Question types: Divisibility and remainders

Rule: Divisibility and remainders

Divisible by 2: ends in an even digit; by 5: ends in 0 or 5; by 10: ends in 0.

By 3 (9): the digit sum is divisible by 3 (9). By 4: the last two digits are divisible by 4.

Example: 837: 8 + 3 + 7 = 18 → divisible by 3 and by 9

Watch out: Divisible by 6 means divisible by 2 and also by 3.

Sample questions

  1. Question 1 Easy

    What is the largest three-digit number divisible by 6?

    Show the solution
    Answer: 996

    How it works: 999 ÷ 6 = 166, remainder 3; 999 − 3 = 996

  2. Question 2 Normal

    What is the smallest digit we can write in place of □ so that 18□3 is divisible by 9?

    Show the solution
    Answer: 6

    How it works: The digit sum must be divisible by 9: 12 + 6 = 18

  3. Question 3 Hard

    How many numbers from 1 to 108 are divisible by at least one of 2 and 8?

    Show the solution
    Answer: 54

    How it works: Divisible by 2: 54, by 8: 13; those divisible by both (multiples of 8) were counted twice: 13; 54 + 13 − 13 = 54

Related topics

All Maths topics

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