Highest Common Factor of 857, 315, 657 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 857, 315, 657 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 857, 315, 657 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 857, 315, 657 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 857, 315, 657 is 1.

HCF(857, 315, 657) = 1

HCF of 857, 315, 657 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 857, 315, 657 is 1.

Highest Common Factor of 857,315,657 using Euclid's algorithm

Highest Common Factor of 857,315,657 is 1

Step 1: Since 857 > 315, we apply the division lemma to 857 and 315, to get

857 = 315 x 2 + 227

Step 2: Since the reminder 315 ≠ 0, we apply division lemma to 227 and 315, to get

315 = 227 x 1 + 88

Step 3: We consider the new divisor 227 and the new remainder 88, and apply the division lemma to get

227 = 88 x 2 + 51

We consider the new divisor 88 and the new remainder 51,and apply the division lemma to get

88 = 51 x 1 + 37

We consider the new divisor 51 and the new remainder 37,and apply the division lemma to get

51 = 37 x 1 + 14

We consider the new divisor 37 and the new remainder 14,and apply the division lemma to get

37 = 14 x 2 + 9

We consider the new divisor 14 and the new remainder 9,and apply the division lemma to get

14 = 9 x 1 + 5

We consider the new divisor 9 and the new remainder 5,and apply the division lemma to get

9 = 5 x 1 + 4

We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get

5 = 4 x 1 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 857 and 315 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(9,5) = HCF(14,9) = HCF(37,14) = HCF(51,37) = HCF(88,51) = HCF(227,88) = HCF(315,227) = HCF(857,315) .

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

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

657 = 1 x 657 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 657 is 1

Notice that 1 = HCF(657,1) .

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Frequently Asked Questions on HCF of 857, 315, 657 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 857, 315, 657?

Answer: HCF of 857, 315, 657 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 857, 315, 657 using Euclid's Algorithm?

Answer: For arbitrary numbers 857, 315, 657 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.