Highest Common Factor of 617, 391, 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 617, 391, 672 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 617, 391, 672 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 617, 391, 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 617, 391, 672 is 1.

HCF(617, 391, 672) = 1

HCF of 617, 391, 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 617, 391, 672 is 1.

Highest Common Factor of 617,391,672 using Euclid's algorithm

Highest Common Factor of 617,391,672 is 1

Step 1: Since 617 > 391, we apply the division lemma to 617 and 391, to get

617 = 391 x 1 + 226

Step 2: Since the reminder 391 ≠ 0, we apply division lemma to 226 and 391, to get

391 = 226 x 1 + 165

Step 3: We consider the new divisor 226 and the new remainder 165, and apply the division lemma to get

226 = 165 x 1 + 61

We consider the new divisor 165 and the new remainder 61,and apply the division lemma to get

165 = 61 x 2 + 43

We consider the new divisor 61 and the new remainder 43,and apply the division lemma to get

61 = 43 x 1 + 18

We consider the new divisor 43 and the new remainder 18,and apply the division lemma to get

43 = 18 x 2 + 7

We consider the new divisor 18 and the new remainder 7,and apply the division lemma to get

18 = 7 x 2 + 4

We consider the new divisor 7 and the new remainder 4,and apply the division lemma to get

7 = 4 x 1 + 3

We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get

4 = 3 x 1 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 617 and 391 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(7,4) = HCF(18,7) = HCF(43,18) = HCF(61,43) = HCF(165,61) = HCF(226,165) = HCF(391,226) = HCF(617,391) .

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

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

672 = 1 x 672 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 672 is 1

Notice that 1 = HCF(672,1) .

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Frequently Asked Questions on HCF of 617, 391, 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 617, 391, 672?

Answer: HCF of 617, 391, 672 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 617, 391, 672 using Euclid's Algorithm?

Answer: For arbitrary numbers 617, 391, 672 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.