GMAT- Divisibility Rules

Question 1

Divisibility Rule for 2

Answer 1

Rule:
The last digit of the number is even.

Example:
3,576 is even because 6 is an even number.

Question 2

Divisibility Rule for 3

Answer 2

Rule:
The sum of the digits is a multiple of 3.

Example:
4,563 (4+5+6+3 = 18) 18 is multiple of 3
therefore 4563 is a multiple of three.

Question 3

Divisibility Rule for 4

Answer 3

Rule:
The last 2 digits of the number are divisible by 4.

Example:
3,572 is divisible by 4 because 72 is divisible by
4.

708 is divisible by 4 because 08 is divisible by 4.

Question 4

Divisibility Rule for 5

Answer 4

Rule:
The last digit of the number is a five or a zero.

Example:
6,045 is divisible by 5 because it ends in a 5.
867,590 is divisible by 5 because it ends in a
zero.

Question 5

Divisibility Rule for 6

Answer 5

Rule:
The number being tested must work for the rules
of two and three.

Example:
4,266 is divisible by 6 because it ends in an even
number and the sum of its digits.
(4 + 2 + 6 + 6 = 18) is a multiple of 3

Question 6

Divisibility Rule for 7

Answer 6

Rule:
The difference between twice the units digit and
the number that results from removing the units
digit will be a multiple of 7.

Example:
203 is divisible by 7 because 20 (the remaining
number after the 3 is removed) minus 6 (twice
the units digit) is divisible by 7.

Question 7

Divisibility Rule for 8

Answer 7

Rule:
The last 3 digits of the number are divisible by 8.

Example:
4,608 is divisible by 8 because 608 is divisible by
8.

Question 8

Divisibility Rule for 9

Answer 8

Rule:
The sum of the digits is a multiple of 9.

Example:
4,563 (4+5+6+3 = 18) 18 is multiple of 9
therefore 4,563 is a multiple of nine.

Question 9

Divisibility Rule for 10

Answer 9

Rule:
The number being tested ends in zero.

Example:
130 is divisible by 10 because it ends in a zero.

Question 10

Divisibility Rule for 11

Answer 10

Rule:
The sum of the digits in the units, hundreds, ten
thousands … places minus the sum of the digits
in tens, thousands, hundred thousands … places
must be a multiple of 11.

Example:
616 is divisible by eleven because the sum of 1st
and 3rd digits (6+6) minus the sum of the 2nd
digit (1) = 11 and eleven is a multiple of eleven.

A number is divisible by 11 if this is true:
1st Step: Starting from the one’s digit add every other digit
2nd Step: Add the remaining digits together
3rd Step: Subtract 1st Step from the 2nd Step
*If this value is 0 then the number is divisible by 11. If it is not 0 then this is the remainder after
dividing by 11 if it is positive. If the number is negative add 11 to it to get the remainder.
Ex [1] 6613585 is divisible by 11 since (5+5+1+6) – (8+3+6) = 0.