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

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