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Methods to find the HCF
There are different methods to find the HCF of two or more numbers but here we will

learn only two of them. These are:
a. Listing Factors Method b. Long Division Method

listing Factors Method

Write the factors of each number. Then, find the common factors and choose the
highest common factor among them.

example 1. Find the HCF of 12 and 30 using the listing factors method.
Solution.

Step 1. List the factors of the first number, that is 12.

Factors of 12 are 1, 2, 3, 4, 6 and 12.

Step 2. List the factors of the second number, that is 30.
Factors of 30 are 1, 2, 3, 5, 6, 10, 15 and 30.

Step 3. List the common factors of both the numbers.

Common factors of 12 and 30 are 1, 2, 3 and 6.

Step 4. Select the highest common factor, that is 6.
Thus, the highest common factor (HCF) of 12 and 30 is 6.

example 2. Find the HCF of 15, 18 and 24.

Solution. Factors of 15 are 1, 3, 5 and 15.
Factors of 18 are 1, 2, 3, 6, 9 and 18.

Factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24.
Common factors are 1 and 3.

Thus, HCF of 15, 18 and 24 = 3.

long division Method
example 3. Find the HCF of 35 and 80 using the long division method.

Solution. 35 80 2

Step 1. Divide the bigger number (80) by the smaller number – 70
(35). We get Quotient = 2 and Remainder = 10. 10 35 3

Step 2. Take the remainder (10) as the new divisor and the – 30
previous divisor (35) as the new dividend. Divide the 5 10 2

new dividend by the new divisor. – 10
We get Quotient = 3 and Remainder = 5. 0

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Multiples and Factors