Practice Divisibility Intuition in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
Understanding when one whole number divides evenly into another, leaving no remainder—the foundation of factor and multiple relationships.
Can you share 12 cookies equally among 4 people? Yes, 3 each. 12 is divisible by 4.
Showing a random 20 of 50 problems.
Example 1
easyIs divisible by ?
Example 2
easyIs divisible by ?
Example 3
mediumWhy does the last-digit test work for but not for ?
Example 4
hardFind the smallest positive integer that is divisible by .
Example 5
challengeProve the divisibility-by- rule: a number is divisible by iff its digit sum is.
Example 6
mediumIs divisible by ? Show why the -and- check matters.
Example 7
hardFind all digits so that is divisible by .
Example 8
mediumFind the smallest digit so that is divisible by .
Example 9
challengeFind the smallest five-digit number divisible by every integer from to .
Example 10
easyIs divisible by ? By ?
Example 11
mediumContrast the rules: is divisible by and by ? Use digit sums.
Example 12
mediumFill in: a number is divisible by iff its last two digits form one of ____, ____, ____, or ____.
Example 13
easyFind a factor of other than and .
Example 14
mediumIs divisible by ? Check the and conditions.
Example 15
mediumIs divisible by ? Use the last-three-digits rule.
Example 16
mediumIs divisible by ? Use the last-three-digits rule.
Example 17
mediumFind all single-digit factors of .
Example 18
easyUse the digit-sum rule: is divisible by ?
Example 19
mediumIs divisible by ? Check both and .
Example 20
hardIs divisible by ? Use the alternating-sum rule.