Highest Common Factor of 971, 628 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 971, 628 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 971, 628 is 1 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 971, 628 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 971, 628 is 1.

HCF(971, 628) = 1

HCF of 971, 628 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 971, 628 is 1.

Highest Common Factor of 971,628 using Euclid's algorithm

Highest Common Factor of 971,628 is 1

Step 1: Since 971 > 628, we apply the division lemma to 971 and 628, to get

971 = 628 x 1 + 343

Step 2: Since the reminder 628 ≠ 0, we apply division lemma to 343 and 628, to get

628 = 343 x 1 + 285

Step 3: We consider the new divisor 343 and the new remainder 285, and apply the division lemma to get

343 = 285 x 1 + 58

We consider the new divisor 285 and the new remainder 58,and apply the division lemma to get

285 = 58 x 4 + 53

We consider the new divisor 58 and the new remainder 53,and apply the division lemma to get

58 = 53 x 1 + 5

We consider the new divisor 53 and the new remainder 5,and apply the division lemma to get

53 = 5 x 10 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 971 and 628 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(53,5) = HCF(58,53) = HCF(285,58) = HCF(343,285) = HCF(628,343) = HCF(971,628) .

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Frequently Asked Questions on HCF of 971, 628 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 971, 628?

Answer: HCF of 971, 628 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 971, 628 using Euclid's Algorithm?

Answer: For arbitrary numbers 971, 628 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.