Divisibility Intuition Math Example 1

Follow the full solution, then compare it with the other examples linked below.

Example 1

easy
Use divisibility rules to determine whether 4,8364{,}836 is divisible by 22, 33, 44, 66, and 99.

Solution

  1. 1
    By 22: last digit is 66 (even). Yes.
  2. 2
    By 33: digit sum =4+8+3+6=21= 4+8+3+6 = 21; 21÷3=721 \div 3 = 7. Yes.
  3. 3
    By 44: last two digits 3636; 36÷4=936 \div 4 = 9. Yes.
  4. 4
    By 66: divisible by both 22 and 33. Yes.
  5. 5
    By 99: digit sum 2121; 21÷9=2.33…21 \div 9 = 2.33\ldots Not a whole number. No.

Answer

4,8364{,}836 is divisible by 2,3,4,62, 3, 4, 6 but not by 99.
Divisibility rules are shortcuts derived from properties of our base-1010 system. The rules for 22 and 55 check the last digit; for 33 and 99, sum the digits; for 44, check the last two digits. These avoid long division for quick classification.

About Divisibility Intuition

Understanding when one whole number divides evenly into another, leaving no remainder—the foundation of factor and multiple relationships.

Learn more about Divisibility Intuition →

More Divisibility Intuition Examples

Example 2 medium

Explain why the divisibility rule for [formula] works: a number is divisible by [formula] if and onl

Example 3 easy

Test [formula] for divisibility by [formula], [formula], and [formula] using divisibility rules.

Example 4 medium

A number [formula] leaves remainder [formula] when divided by [formula] and remainder [formula] when

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