Highest Common Factor of 382, 971 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 382, 971 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 382, 971 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 382, 971 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 382, 971 is 1.

HCF(382, 971) = 1

HCF of 382, 971 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 382, 971 is 1.

Highest Common Factor of 382,971 using Euclid's algorithm

Highest Common Factor of 382,971 is 1

Step 1: Since 971 > 382, we apply the division lemma to 971 and 382, to get

971 = 382 x 2 + 207

Step 2: Since the reminder 382 ≠ 0, we apply division lemma to 207 and 382, to get

382 = 207 x 1 + 175

Step 3: We consider the new divisor 207 and the new remainder 175, and apply the division lemma to get

207 = 175 x 1 + 32

We consider the new divisor 175 and the new remainder 32,and apply the division lemma to get

175 = 32 x 5 + 15

We consider the new divisor 32 and the new remainder 15,and apply the division lemma to get

32 = 15 x 2 + 2

We consider the new divisor 15 and the new remainder 2,and apply the division lemma to get

15 = 2 x 7 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 382 and 971 is 1

Notice that 1 = HCF(2,1) = HCF(15,2) = HCF(32,15) = HCF(175,32) = HCF(207,175) = HCF(382,207) = HCF(971,382) .

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Frequently Asked Questions on HCF of 382, 971 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 382, 971?

Answer: HCF of 382, 971 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 382, 971 using Euclid's Algorithm?

Answer: For arbitrary numbers 382, 971 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.