Highest Common Factor of 997, 657, 876 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 997, 657, 876 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 997, 657, 876 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 997, 657, 876 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 997, 657, 876 is 1.

HCF(997, 657, 876) = 1

HCF of 997, 657, 876 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 997, 657, 876 is 1.

Highest Common Factor of 997,657,876 using Euclid's algorithm

Highest Common Factor of 997,657,876 is 1

Step 1: Since 997 > 657, we apply the division lemma to 997 and 657, to get

997 = 657 x 1 + 340

Step 2: Since the reminder 657 ≠ 0, we apply division lemma to 340 and 657, to get

657 = 340 x 1 + 317

Step 3: We consider the new divisor 340 and the new remainder 317, and apply the division lemma to get

340 = 317 x 1 + 23

We consider the new divisor 317 and the new remainder 23,and apply the division lemma to get

317 = 23 x 13 + 18

We consider the new divisor 23 and the new remainder 18,and apply the division lemma to get

23 = 18 x 1 + 5

We consider the new divisor 18 and the new remainder 5,and apply the division lemma to get

18 = 5 x 3 + 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 997 and 657 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(18,5) = HCF(23,18) = HCF(317,23) = HCF(340,317) = HCF(657,340) = HCF(997,657) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Step 1: Since 876 > 1, we apply the division lemma to 876 and 1, to get

876 = 1 x 876 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 876 is 1

Notice that 1 = HCF(876,1) .

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Frequently Asked Questions on HCF of 997, 657, 876 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 997, 657, 876?

Answer: HCF of 997, 657, 876 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 997, 657, 876 using Euclid's Algorithm?

Answer: For arbitrary numbers 997, 657, 876 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.