Highest Common Factor of 391, 408 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, 408 i.e. 17 the largest integer that leaves a remainder zero for all numbers.

HCF of 391, 408 is 17 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, 408 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, 408 is 17.

HCF(391, 408) = 17

HCF of 391, 408 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

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Highest common factor (HCF) of 391, 408 is 17.

Highest Common Factor of 391,408 using Euclid's algorithm

Highest Common Factor of 391,408 is 17

Step 1: Since 408 > 391, we apply the division lemma to 408 and 391, to get

408 = 391 x 1 + 17

Step 2: Since the reminder 391 ≠ 0, we apply division lemma to 17 and 391, to get

391 = 17 x 23 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 17, the HCF of 391 and 408 is 17

Notice that 17 = HCF(391,17) = HCF(408,391) .

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Frequently Asked Questions on HCF of 391, 408 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, 408?

Answer: HCF of 391, 408 is 17 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 391, 408 using Euclid's Algorithm?

Answer: For arbitrary numbers 391, 408 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.