Signs of divisibility by 3, 6 and 9

Sign of divisibility by 3

A number is divisible by 3 if the sum of all its digits is divisible by 3.

Examples:

• 153 is divided by 3. The sum of all its digits: 1 + 5 + 3 = 9 is divided by 3 (9: 3 = 3).
• 300 is divided by 3. The sum of all its digits: 3 + 0 + 0 = 3 is divided by 3 (3: 3 = 1).
• 11 is not divisible by 3. The sum of all its digits: 1 + 1 = 2 is not divisible by 3.

Sign of divisibility by 6

A number is divisible by 6 if it is divisible by 2 and 3 at the same time.

Examples:

• 126 is divisible by 6. Based on divisibility by 2, it is divisible by 2 (the last 6 is divisible by 2). On the basis of divisibility by 3, it is also divided by 3 (the sum of the digits of the number 1 + 2 + 6 = 9 is divided by three). This means that 126 is divisible by 6.
• 801 is not divisible by 6. Based on divisibility by 2, it is not divisible by 2.
• 757 is not divisible by 6. Based on divisibility by 3, it is not divisible by 3.

Sign of divisibility by 9

A number is divisible by 9 if the sum of all its digits is divisible by 9.

Examples:

• 486 is divisible by 9. The sum of all its digits: 4 + 8 + 6 = 18 is divisible by 9 (18: 9 = 2).
• 9198 is divisible by 9. The sum of all its digits: 9 + 1 + 9 + 8 = 27 is divisible by 9 (27: 9 = 3).
• 55 is not divisible by 9. The sum of all its digits: 5 + 5 = 10 is not divisible by 9.