Highest Common Factor of 6171, 8465 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 6171, 8465 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 6171, 8465 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 6171, 8465 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 6171, 8465 is 1.

HCF(6171, 8465) = 1

HCF of 6171, 8465 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 6171, 8465 is 1.

Highest Common Factor of 6171,8465 using Euclid's algorithm

Highest Common Factor of 6171,8465 is 1

Step 1: Since 8465 > 6171, we apply the division lemma to 8465 and 6171, to get

8465 = 6171 x 1 + 2294

Step 2: Since the reminder 6171 ≠ 0, we apply division lemma to 2294 and 6171, to get

6171 = 2294 x 2 + 1583

Step 3: We consider the new divisor 2294 and the new remainder 1583, and apply the division lemma to get

2294 = 1583 x 1 + 711

We consider the new divisor 1583 and the new remainder 711,and apply the division lemma to get

1583 = 711 x 2 + 161

We consider the new divisor 711 and the new remainder 161,and apply the division lemma to get

711 = 161 x 4 + 67

We consider the new divisor 161 and the new remainder 67,and apply the division lemma to get

161 = 67 x 2 + 27

We consider the new divisor 67 and the new remainder 27,and apply the division lemma to get

67 = 27 x 2 + 13

We consider the new divisor 27 and the new remainder 13,and apply the division lemma to get

27 = 13 x 2 + 1

We consider the new divisor 13 and the new remainder 1,and apply the division lemma to get

13 = 1 x 13 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 6171 and 8465 is 1

Notice that 1 = HCF(13,1) = HCF(27,13) = HCF(67,27) = HCF(161,67) = HCF(711,161) = HCF(1583,711) = HCF(2294,1583) = HCF(6171,2294) = HCF(8465,6171) .

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Frequently Asked Questions on HCF of 6171, 8465 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 6171, 8465?

Answer: HCF of 6171, 8465 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 6171, 8465 using Euclid's Algorithm?

Answer: For arbitrary numbers 6171, 8465 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.