Highest Common Factor (HCF)

The greatest number which divides two or more numbers exactly without leaving any remainder is called HCF.

We can find the HCF by two methods:

a)prime factorisation method

b) division method

a) HCF by Prime Factorisation Method :

To find the HCF by prime factorisation, we find the prime factors of the given numbers and list the prime factors which are common in all. The product of the common prime factors is the required HCF.

Example: Find the HCF of 18, 24, 42.

Prime factors of 18 = 2 \times 3 \times 3

Prime factors of 24 = 2 \times 2 \times 2 \times 3

Prime factors of 24 = 2 \times 3  \times 7

Common prime factors are = 2 and 3

HCF = 2 \times 3 = 6

b) HCF by Long Division Method :

Step 1 : Make the smaller number as divisor and the larger number as dividend and start dividing.

Step 2 : The remainder left (if not zero) becomes the new divisor and the last divisor becomes the dividend.

Step 3 : Continue the process till a zero remainder is obtained.

Example : The HCF of 72 and 192 is 24.

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