Highest Common Factor of 391, 659 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 391, 659 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 391, 659 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 391, 659 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 391, 659 is 1.

HCF(391, 659) = 1

HCF of 391, 659 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 391, 659 is 1.

Highest Common Factor of 391,659 using Euclid's algorithm

Highest Common Factor of 391,659 is 1

Step 1: Since 659 > 391, we apply the division lemma to 659 and 391, to get

659 = 391 x 1 + 268

Step 2: Since the reminder 391 ≠ 0, we apply division lemma to 268 and 391, to get

391 = 268 x 1 + 123

Step 3: We consider the new divisor 268 and the new remainder 123, and apply the division lemma to get

268 = 123 x 2 + 22

We consider the new divisor 123 and the new remainder 22,and apply the division lemma to get

123 = 22 x 5 + 13

We consider the new divisor 22 and the new remainder 13,and apply the division lemma to get

22 = 13 x 1 + 9

We consider the new divisor 13 and the new remainder 9,and apply the division lemma to get

13 = 9 x 1 + 4

We consider the new divisor 9 and the new remainder 4,and apply the division lemma to get

9 = 4 x 2 + 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 391 and 659 is 1

Notice that 1 = HCF(4,1) = HCF(9,4) = HCF(13,9) = HCF(22,13) = HCF(123,22) = HCF(268,123) = HCF(391,268) = HCF(659,391) .

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Frequently Asked Questions on HCF of 391, 659 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 391, 659?

Answer: HCF of 391, 659 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 391, 659 using Euclid's Algorithm?

Answer: For arbitrary numbers 391, 659 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.