Highest Common Factor of 676, 208 using Euclid's algorithm

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 676, 208 i.e. 52 the largest integer that leaves a remainder zero for all numbers.

HCF of 676, 208 is 52 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.

Consider we have numbers 676, 208 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b

Highest common factor (HCF) of 676, 208 is 52.

HCF(676, 208) = 52

HCF of 676, 208 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

HCF of:

Highest common factor (HCF) of 676, 208 is 52.

Highest Common Factor of 676,208 using Euclid's algorithm

Highest Common Factor of 676,208 is 52

Step 1: Since 676 > 208, we apply the division lemma to 676 and 208, to get

676 = 208 x 3 + 52

Step 2: Since the reminder 208 ≠ 0, we apply division lemma to 52 and 208, to get

208 = 52 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 52, the HCF of 676 and 208 is 52

Notice that 52 = HCF(208,52) = HCF(676,208) .

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Frequently Asked Questions on HCF of 676, 208 using Euclid's Algorithm

1. What is the Euclid division algorithm?

Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.

2. what is the HCF of 676, 208?

Answer: HCF of 676, 208 is 52 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 676, 208 using Euclid's Algorithm?

Answer: For arbitrary numbers 676, 208 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.