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Divisibility Rules - Finding Factors

Rules for Finding Factors

1 is a factor of every number

2 is a factor of a number when the last digit of the number is even; in other words, the last digit is 0, 2, 4, 6, or 8. For example 35, 578 has 2 as a factor.

3 is a factor of a number when three is a factor of the sum of the digits in that number. Example 4221 has a factor of 3, since 4 + 2 + 2 + 1 = 9 and 3 is a factor of 9. However, 3 is not a factor of 356, since 3 + 5 + 6 =14, and 3 is not a factor of 14.

4 is a factor of a number when the last two digits of the number also have four as a factor. For instance, 5728 has 4 as a factor since 4 is a factor of 28.

5 is a factor of a number when the last digit is either 0 or 5. Example 6785 has a factor of 5.

6 is a factor of a number when two conditions are met. The last digit is even AND the sum of the digits has a factor of 3.

7 is a factor of a number when 7 is a factor of . Study carefully. Let's look at 553. Remove the last number, 3. The number becomes 55. Double 3 to get 6 . Then subtract from 55. So, 55 6 = 49. Since 7 is a factor of 49, seven is a factor of the original number 553.

8 - is a factor of a number when 8 is a factor of the number the last three digits represent. For example, 4528 has 8 as a factor because 8 is a factor of 528.

9 is a factor of a number when 9 is a factor of the sum of digits in that number. For example, 7542 has 9 as a factor because 7 + 5 + 4 + 2 = 18, and 9 is a factor of 18.

10 is a factor of a number when the last digit is 0. For example, 20 and 346,690 both have 10 as a factor.




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