Highest Common Factor of 317, 874 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 317, 874 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 317, 874 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 317, 874 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 317, 874 is 1.

HCF(317, 874) = 1

HCF of 317, 874 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 317, 874 is 1.

Highest Common Factor of 317,874 using Euclid's algorithm

Highest Common Factor of 317,874 is 1

Step 1: Since 874 > 317, we apply the division lemma to 874 and 317, to get

874 = 317 x 2 + 240

Step 2: Since the reminder 317 ≠ 0, we apply division lemma to 240 and 317, to get

317 = 240 x 1 + 77

Step 3: We consider the new divisor 240 and the new remainder 77, and apply the division lemma to get

240 = 77 x 3 + 9

We consider the new divisor 77 and the new remainder 9,and apply the division lemma to get

77 = 9 x 8 + 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 317 and 874 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(9,5) = HCF(77,9) = HCF(240,77) = HCF(317,240) = HCF(874,317) .

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Frequently Asked Questions on HCF of 317, 874 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 317, 874?

Answer: HCF of 317, 874 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 317, 874 using Euclid's Algorithm?

Answer: For arbitrary numbers 317, 874 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.