How to Know if a Number is Divisible By Nine
Divisibility rules come in handy for taking shortcuts in tedious math calculations such as classifying numbers as prime or composite or reducing fractions to lowest terms. Divisibility means that when you divide one number by another number, the quotient or answer will be a whole number with no remainder. When you need to know if a number is divisible by nine, simple addition will answer the question without having to resort to manual long division.
- Difficulty:
- Easy
Instructions
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1
Look at each digit in a number such as 6,450 or 8,271.
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2
Add the digits of a number together and write down the sum. For example, for 6,450, 6 + 4 + 5 + 0 = 15; or for 8,271, 8 + 2 + 7 + 1 = 18.
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Check your sum against common products on the multiplication table. Any of the products in the 9's column are divisible by 9 because of the inverse relationship of multiplication and division. In other words, one operation reverses the other. If the sum of the digits of the original number is divisible by nine then, the larger number is as well. Nine divides equally into 18 but not 15. Therefore, 8,271 is divisible by nine but 6,450 is not.
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Tips & Warnings
With large numbers such as 98,976,897, you can add the digits of the sum in succession until it breaks down to a number clearly divisible by 9. For example, 9 + 8 + 9 + 7 + 6 + 8 + 9 + 7 equals 63. If you aren't sure whether 63 is divisible by nine, continue adding 6 + 3 to get 9. Nine is clearly divisible by itself so the large number is also divisible by nine.
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