Rules of divisibility test

A number is divisible by:

• 2: if the last digit of the number is even or zero.
• 3: if the sum of the digits is divisible by 3.
• 4: if the number formed by the last 2 digits is divisible by 4.
• 5: if the numbers end in 0 or 5.
• 6: if the number is divisible by both 2and 3.
• 7: no rule to it yet.
• 8: if the number formed by the last three digits of the numbers is divisible by 8.
• 9: if the sum of the digits is divisible by 9 and 3.
• 10: if the last digit is zero.
• 11: if the sum of the digits in the odd positions is equal to the sum of digits in the even positions or difference is a multiple of 11.

DIVISIBILITY test is a rule for determining whether one whole number is divisible by another.

EXAMPLE

Determine whether 7168 is divisible by2, 3, 4,5,6,8,9,10 and 11

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SOLUTION

7168 Is not divisible by 3, 5, 6, 9, 10 and 11. But 2 because the last digit is even, 4 since the last twodigits is divisible by 4. 8 since the last three digit is divisible by 8.

EXAMPLE

Which number is divisible by 35120?

SOLUTION

35120 is divisible by 2,4,5,8and 10.

2 can divide it since it end with zero, divisible by 4, since the last two digit 20 is divisible by 4, 5 since it end with zero, 8 since the last digit 120 is divisible by 8. 10 since the last digit is zero.

EXAMPLE

Determine whether 24739 is divisible by 11?

SOLUTION

24739→sum of digit in odd position 2+7+9=18, sum of digit in even position 4+3=7. Thedifference18-7=11. Then 11 is divisible by 11 and a multiple of 11.

CLASS WORK

Identify the following numbers that can be divisible by 2,4 ,5 , 6,8, 9.

a.3591 b. 2408 c. 7700 d. 18054 e.2032  f. 1827 g.23624 h. 468

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