# New Rule for Divisibility of 8

Old- A number is divisible by 8 if the last 3 digits is divisible by 8.

This rule is actually difficult to test because students are required to know the multiples of 8 between 100 and 1000 that is three-digit numbers.

Proposed New Rule: A number is divisible by 8 if the SUM of the number formed by the last two digits and 4 times the hundred digit is divisible by 8

Examples: To test whether 8 can divide the following numbers- 112, 536, 708, 7152 .

1. To test 112, separate 112 into 1 and 12. Multiply 1 by 4 and add it to 12 which now gives 4 + 12 = 16. Since 16 is divisible by 8, then 112 is divisible by 8
1. To test 536, separate 536 into 5 and 36. Multiply 5 by 4 and add it to 36 which gives 20 + 36 = 56 a number divisible by 8. Therefore 536 is divisible by 8.
1. To test 708, separate 708 into 7 and 08. Multiply 7 by 4 and add it to 8 which gives 28 + 8 = 36 a number not divisible by 8. Therefore 708 is not divisible by 8.
1. To test 7152, test only the last 3 digits – that is 152. Separate 152 into 1 and 52. Multiply 1 by 4 and add it to 52 which gives 4 + 52 = 56 a number divisible by 8. Therefore 7152 is divisible by 8.