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Highest Common Factor

Find the highest common factor of 36 and 84. Find the answer to this question and access a vast question bank customised for students.

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Q. Find the Highest Common Factor of 36 and 84

The greatest number among all the common factors of two or more numbers is known as HCF (Highest Common Factor)
The methods to find the HCF of 36 and 84 are given below:

1. Long Division Method
2. Prime Factorization Method
3. Using Euclid’s Algorithm

Finding HCF of 36 and 84 by using the long division method

1. Firstly, Divide 84 (larger number) by 36 (smaller number).
2. Secondly, Since the remainder ≠ 0, we will divide the divisor of step 1 (36) by the remainder (12).
3. Thirdly, Repeat the above-mentioned process until the remainder = 0.
4. The corresponding divisor (12) is the HCF of 36 and 84.

Finding HCF of 36 and 84 by using Prime Factorization Method

1. Prime factorization of 36 = (2 × 2 × 3 × 3) and 84= (2 × 2 × 3 × 7)
2. common prime factors of 36 and 84 are 2, 2, and 3.
3. Hence, the HCF of 36 and 84 is 2 × 2 × 3 = 12.

Finding HCF of 36 and 84 by using Euclid’s Algorithm

According to Euclidean Algorithm, HCF (X, Y) = HCF (Y, X mod Y)

where X > Y and the mod is the modulo operator.

Here, X = 84 and Y = 36

- HCF (84, 36) = HCF (36, 84 mod 36) = HCF (36, 12)
- HCF (36, 12) = HCF (12, 36 mod 12) = HCF (12, 0)
- HCF (12, 0) = 12 (∵ HCF (X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 36 and 84 is 12.