Highest Common Factor of 631, 416 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 631, 416 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 631, 416 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 631, 416 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 631, 416 is 1.

HCF(631, 416) = 1

HCF of 631, 416 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 631, 416 is 1.

Highest Common Factor of 631,416 using Euclid's algorithm

Highest Common Factor of 631,416 is 1

Step 1: Since 631 > 416, we apply the division lemma to 631 and 416, to get

631 = 416 x 1 + 215

Step 2: Since the reminder 416 ≠ 0, we apply division lemma to 215 and 416, to get

416 = 215 x 1 + 201

Step 3: We consider the new divisor 215 and the new remainder 201, and apply the division lemma to get

215 = 201 x 1 + 14

We consider the new divisor 201 and the new remainder 14,and apply the division lemma to get

201 = 14 x 14 + 5

We consider the new divisor 14 and the new remainder 5,and apply the division lemma to get

14 = 5 x 2 + 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 631 and 416 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(14,5) = HCF(201,14) = HCF(215,201) = HCF(416,215) = HCF(631,416) .

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Frequently Asked Questions on HCF of 631, 416 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 631, 416?

Answer: HCF of 631, 416 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 631, 416 using Euclid's Algorithm?

Answer: For arbitrary numbers 631, 416 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.