 Divisibility Rules - Orchids The International School Factors and Multiples

Divisibility Rules

The divisibility rules are the short-hand rules to identify if the given integers are divisible by the divisor.

List of divisibility rules

• Divisible by 2:

• A number is said to be divisible by 2 if the last digits of the number is 0, 2, 4, 6 and 8.
• Examples:24, 380, 4502 are divisible by 2.

• Divisible by 3:

• A number is said to be divisible by 3 if the sum of the digits is divisible by 3
• Examples: Consider the number 342. The sum of the digits is 3 + 4 + 2 = 9 Since the number 9 is divisible by 3. Therefore, 342 is also divisible by 3.

• Divisible by 4:

• A number is said to be divisible by 4 if the last two digits of the number is divisible by 4.
• Examples:Consider the number 420.

• The last two digits of the number is 20.

Since the number 20 is divisible by 4. Therefore, 420 is also divisible by 4.

• Divisible by 5:

• A number is said to be divisible by 5 if the last digits of the number is either 0 or 5.
• Examples:25, 340, 765 are divisible by 5.

• Divisible by 6:

• A number is said to be divisible by 6 if it is divisible by both 2 and 3.
• Examples:Consider the number 84.

• The last digit is 4, 84 is divisible by 2.

The sum of the digit is 8 + 4 = 12. The number 12 is divisible by 3. Therefore, 84 is divisible by 3.

The number 84 is divisible by both 2 and 3. Therefore, 84 is also divisible by 6.

• Divisible by 9:

• A number is said to be divisible by 9 if the sum of the digits is divisible by 9.
• Examples:Consider the number 342.

• The sum of the digits is 3 + 4 + 2 = 9

Since the number 9 is divisible by 9. Therefore, 342 is also divisible by 9.

• Divisible by 10:

• A number is said to be divisible by 10 if the last digits of the number is 0.
• Examples:240, 380, 450 are divisible by 10.

Examples: Prime Factorization

• The process of breaking down the number as the product of prime numbers.
• The two methods of prime factorization are:
• Factor Tree
• Division Method

Factor Tree

Factor tree is a tree diagram which is used to find the prime factors of a number

Steps to draw a factor tree:

• Each branch of the tree is split into two factors.
• It stops when the factors at the end of the branch is a prime number.

Examples: • In the above example, it is observed that:
• The product of 6 and 18 is equal to 108. Therefore, the 6 and 18 are the factors of 108.
• The numbers 2 and 3 are the prime numbers. So, the factor tree stops.
• Therefore, 108 = 2 × 2 × 3 × 3 × 3.

Division Method

It is a process of finding the prime factors of a number by dividing the number.

Steps for the division method of prime factorization:

• Divide the number by the smallest prime numbers.
• Repeat the process till we get 1 as a factor.

Examples: • In the above example the number 64 is first divided by the smallest prime number which is 2.
• Then 32 is divided by the smallest prime number 2 to get 16.
• The process of division is continued unit we get 1 as a factor.
• Therefore, 64 = 2 × 2 × 2 × 2 × 2 × 2

Commom Mistakes:

While making a factor tree the most common mistake is that the numbers are split in such a way that their sum is equal to the number.

Examples:  • -