Division Method for finding HCF of 84 and 108:

To find the HCF of 84 and 108 by the division method, we follow the below steps:

Step 1: We divide the larger number i.e. 108 by the smaller number i.e. 84. We get the quotient and remainder.

108 ÷ 84 = 1 (quotient) and 24 (remainder)

Step 2: Now we divide the divisor i.e. 84 by the remainder obtained in the previous step i.e. 24.

84 ÷ 24 = 3 (quotient) and 12 (remainder)

Step 3: We again divide the divisor i.e. 24 by the remainder obtained in the previous step i.e. 12.

24 ÷ 12 = 2 (quotient) and 0 (remainder)

Step 4: As we get a remainder of zero in the last step, we stop the division process.

Step 5: The divisor in the last step i.e. 12 is the required HCF of 84 and 108.

Therefore, HCF of 84 and 108 is 12.

Explanation:

In the division method, we divide the larger number by the smaller number. Then we divide the divisor obtained in the first step by the remainder obtained in the first step. We keep on repeating this process until we get a remainder as zero. The divisor in the last step is the HCF of the given numbers.

In this case, we first divided 108 by 84 to get a remainder of 24. Then we divided 84 by 24 to get a remainder of 12. Finally, we divided 24 by 12 to get a remainder of zero. Therefore, the divisor obtained in the last step i.e. 12 is the HCF of 84 and 108.

The division method is an easy and quick method to find the HCF of two numbers. It is also known as the Euclidean algorithm.

Step 1. applying euclid's division lemma to 84 and 108 we get.............108=84×1+24..........step2.applying euclid's division lemma to 84 and 24 we get......84=24×3+12.........step3. now applying euclids division lemma to 12 and 24 we get 24=12×2+0.........so the HCF(84,108)=12