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Finding HCF of Numbers

We can find the HCF of two or more numbers by any of the three methods:

1. Common factors method 2. Prime factorisation method 3. Long division method
Common Factors Method

Follow these steps for finding HCF of two or more numbers by common factor method.

Step 1: List the factors of given numbers.
Step 2: List the common factors of given numbers.

Step 3: Write the highest of the common factors as HCF.
Example 21: Find the HCF of 36, 60 and 84.

Solution: Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18 and 36.
Factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60.

Factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42 and 84.
Common factors are 1, 2, 3, 4, 6 and 12.

12 is the greatest among these common factors.
Hence, the HCF of 36, 60 and 84 is 12.

Prime Factorisation Method

Follow these steps for finding HCF of two or more numbers by prime factorisation method.
Step 1: Express each number as a product of its prime factors.

Step 2: Write the common prime factors of the numbers.
Step 3: Find the product of common prime factors. This is the HCF of given numbers.

Example 22: Find the HCF of 70, 105 and 175.
Solution: By getting prime factorisation of these numbers,

2 70 3 105 5 175

5 35 5 35 5 35
7 7 7

70 = 2 × 5 × 7 105 = 3 × 5 × 7 175 = 5 × 5 × 7

The common prime factors of 70, 105 and 175 are 5 and 7.
Thus, HCF of 70, 105 and 175 is 5 × 7 = 35.
Long Division Method

Follow these steps to find the HCF of two or more numbers by long division method.
Step 1: Divide the bigger number by the smaller number.
Step 2: The remainder becomes the divisor and the first divisor is the new dividend.

Step 3: Continue in this way till the remainder is 0. The last divisor is the HCF.

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