Highest Common Factor of 728, 672 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 728, 672 i.e. 56 the largest integer that leaves a remainder zero for all numbers.

HCF of 728, 672 is 56 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 728, 672 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 728, 672 is 56.

HCF(728, 672) = 56

HCF of 728, 672 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 728, 672 is 56.

Highest Common Factor of 728,672 using Euclid's algorithm

Highest Common Factor of 728,672 is 56

Step 1: Since 728 > 672, we apply the division lemma to 728 and 672, to get

728 = 672 x 1 + 56

Step 2: Since the reminder 672 ≠ 0, we apply division lemma to 56 and 672, to get

672 = 56 x 12 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 56, the HCF of 728 and 672 is 56

Notice that 56 = HCF(672,56) = HCF(728,672) .

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Frequently Asked Questions on HCF of 728, 672 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 728, 672?

Answer: HCF of 728, 672 is 56 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 728, 672 using Euclid's Algorithm?

Answer: For arbitrary numbers 728, 672 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.