### Math Notes

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Basic Mathematics Solved Problems | Topics - Contents

# Divisibility Rules

Related topics: Factors and Multiples
We would like to find the number that will divide a given number with out any remainder. Below are the different rules on how we can check if a given number can be divided by the following numbers.
Number (n) Number (n) can Divide a given number if:
2 The number ends with 0, 2, 4, 6 or 8.
Example 582 is divible by 2 because it ends with 2
3 The sum of the digits are divisible by 3.
123 is divisible by 3 because 1+2+3 = 6 and 6 is divisible by 3.
4 The last two digits of a number is divisble by 4 or the last two digits are both zero.
8900 is divisible by 4 because it ends with two zeroes. 81912 is also divisble by 4 because 12(the last two digits) is divisible by 4.
5 The last digit of the number ends with 0 or 5.
155 is divisible by 5 because it end with 5.
6 If the number is divisble by both 3 and 2.
72 is divisible by 6 because 3 and 2 are multiples of 72.
7 If subtracting twice the last digit of the number from the remaining digits is divisible 7.
98 is divisible by 7 because 8 x 2 = 16 and 16-9= 7 and 7 is divisible by 7
8 If the las three digit of the number is divisible by 8.
1280 is divisble by 8 because 280/8 = 35
9 If the sum of the digits is divisible by 9.
585 is divisible by 9 because 5 + 8 + 5 = 18 and 18/9 = 2
10 If the number ends with zero.
1050 is divisible by 10 because the number ends with 0.
11 If the difference of the alternating sum of the digits of the number is 0 or divisible by 11.
1078 is divisible by 11 because 1+7 = 8, 0+8 = 8 and 8-8 = 0.
12 If the number is divisible by both 4 and 3