Divisibility Rules for 3, 6, and 9

Divisibility Rules

Divisibility By 3

• A number is divisible by 3 if the sum of its digits is divisible by 3.
• Example: 123 is divisible by 3 because 1 + 2 + 3 = 6, which is divisible by 3.

Divisibility By 9

• A number is divisible by 9 if the sum of its digits is divisible by 9.
• Example: 459 is divisible by 9 because 4 + 5 + 9 = 18, which is divisible by 9.

Divisibility By 6

• A number is divisible by 6 if it is divisible by both 2 and 3.
• A number is divisible by 2 if it ends in 0, 2, 4, 6, or 8.
• Combine the rules for divisibility by 2 and 3 to check for divisibility by 6.
• Example: 120 is divisible by 6 because it ends in 0 (divisible by 2) and 1 + 2 + 0 = 3, which is divisible by 3.

Prime Factors

• A prime factor is a prime number that divides a given number exactly without leaving a remainder.
• Every composite number can be expressed as a product of prime factors in a unique way.
• Example: The prime factors of 12 are 2, 2, and 3 because 2 × 2 × 3 = 12.

Remainders

• A remainder is the amount left over when one number is divided by another.
• When dividing a number by a divisor, the remainder is always less than the divisor.
• Example: When dividing 17 by 5, the quotient is 3 and the remainder is 2 because 17 = 3 × 5 + 2.

Divisibility Rules

Divisibility By 3

• A number is divisible by 3 if the sum of its digits is divisible by 3.
• The sum of digits is calculated by adding up individual digits of the number.
• Example: 123 is divisible by 3 because 1 + 2 + 3 = 6, which is divisible by 3.

Divisibility By 9

• A number is divisible by 9 if the sum of its digits is divisible by 9.
• The sum of digits is used to determine divisibility by 9.
• Example: 459 is divisible by 9 because 4 + 5 + 9 = 18, which is divisible by 9.

Divisibility By 6

• A number is divisible by 6 if it is divisible by both 2 and 3.
• A number is divisible by 2 if it ends in 0, 2, 4, 6, or 8.
• Combine the rules for divisibility by 2 and 3 to check for divisibility by 6.
• Example: 120 is divisible by 6 because it ends in 0 (divisible by 2) and 1 + 2 + 0 = 3, which is divisible by 3.

Prime Factors

• A prime factor is a prime number that divides a given number exactly without leaving a remainder.
• Every composite number can be expressed as a product of prime factors in a unique way.
• Example: The prime factors of 12 are 2, 2, and 3 because 2 × 2 × 3 = 12.

Remainders

• A remainder is the amount left over when one number is divided by another.
• The remainder is always less than the divisor.
• Example: When dividing 17 by 5, the quotient is 3 and the remainder is 2 because 17 = 3 × 5 + 2.