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Divisibility and Mental Math Rules Explained

Learn about divisibility rules and mental math techniques to determine if a number is divisible by another. Discover how to apply rules for 2, 3, 5, 9, and 10 to identify factors. Practice examples included for better understanding.

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Divisibility and Mental Math Rules Explained

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  1. Divisibility and Mental Math

  2. Vocabulary A number is divisible by another number if it can be divided into and result in a remainder of 0. 24 is divisible by 4, because 24 ÷ 4 = 6. 24 is not divisible by 5, because 24 ÷ 5 = 4.8 (or 4R4). An even number ends with a 0, 2, 4, 6, or 8. An odd number ends with a 1, 3, 5, 7, or 9.

  3. Divisibility Rules 2 divides into all even numbers. 3 divides into a number if the sum of the digits of that number is divisible by 3. 5 divides into numbers that end with a 5 or 0. 9 divides into a number if the sum of the digits of that number is divisible by 9. 10 divides into numbers that end with 0.

  4. Example: Test each number for divisibility by 3. 216 2 + 1 + 6 = 9 9 is divisible by 3, so 216 is divisible by 3. yes 437 4 + 3 + 7 = 14 14 is not divisible by 3, so 437 is not divisible by 3. no

  5. Example: Test the number for divisibility by 2, 5, or 10. 454,320 2 works because the number is even. 5 works because the number ends with 0. 10 works because the number ends with 0. 4 + 5 + 4 + 3 + 2 + 0 = 18. Is the number divisible by 9? 18 is divisible by 9, so 454,320 is also divisible by 9.

  6. Homework Time

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