Divisibility Rules

A number is divisible by another number when the quotient is a whole number—a number with no remainder.

When a number is divisible by another number, the quotient is...

• has a remainder

• is less than 1

• is larger than the dividend

• is a whole number

Divisibility rules are rules that can be used as a quick test to figure out if one number is divisible by another. Divisibility rules let us determine divisibility without actually calculating a quotient.

Every even number is divisible by 2

In which choice below are ALL of the numbers divisible by 2?

• 32, 72, 856, 401

• 84, 92, 850, 396

• 92, 86, 461, 982

Divisibility rules are rules that can be used as a quick test to figure out if one number is divisible by another. Divisibility rules let us determine divisibility without actually calculating a quotient.

If the sum of all digits in a number is divisible by 3, that number is divisible by 3.

In which choice below, are ALL of the numbers divisible by 3?

• 93, 105, 333

• 80, 93, 180

• 45, 600, 41

Divisibility rules are rules that can be used as a quick test to figure out if one number is divisible by another. Divisibility rules let us determine divisibility without actually calculating a quotient.

If the last two digits of a number are divisible by 4, that number is divisible by 4.



In which choice below are ALL of the numbers divisible by 4?

• 724, 616, 810

• 932, 804, 414

• 512, 908, 724

Divisibility rules are rules that can be used as a quick test to figure out if one number is divisible by another. Divisibility rules let us determine divisibility without actually calculating a quotient.

Every number that ends in 0 or 5 is divisible by 5.



In which choice below are ALL of the numbers divisible by 5?

• 625, 980, 754

• 935, 840, 295

• 450, 655, 901

The divisibility rule for 6 is more complicated. If a number’s last digit is even and the sum of its digits is divisible by 3, that number is divisible by 6. In other words, if a number passes the test for both 2 and 3, it is divisible by 6. For example, we know 72 is divisible by 6 because its last digit, 2, is an even number, and the sum of its digits, 9, is divisible by 3.

In which of the choices below are BOTH of the numbers divisible by 6?

• 235, 450

• 360, 138

• 901, 567

If the sum of all digits in a number is divisible by 9, that number is divisible by 9.  Which choice below is correct?

            

• 8,145 = 8 + 1 + 4 + 5 = 18, 18  $\div$   9 = 2,  so 8,145 is divisible by 9

• 8,143 = 8 + 1 + 4 + 3 = 16,  16  $\div$  9 = 2, so 8,143 is divisible by 9

Every number that ends in 0 is divisible by 10.

Which of these numbers is NOT divisible by 10?

• 14,940

• 723,450

• 25,910

• 923,720

• 870,123

A number is divisible by another number when the quotient...

• is a decimal

• is an even number

• has no remainder

• is zero

True or False: Not every whole number is divisible by 1.

• True

• False