Highest Common Factor of 8966, 657 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 8966, 657 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 8966, 657 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 8966, 657 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 8966, 657 is 1.

HCF(8966, 657) = 1

HCF of 8966, 657 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 8966, 657 is 1.

Highest Common Factor of 8966,657 using Euclid's algorithm

Highest Common Factor of 8966,657 is 1

Step 1: Since 8966 > 657, we apply the division lemma to 8966 and 657, to get

8966 = 657 x 13 + 425

Step 2: Since the reminder 657 ≠ 0, we apply division lemma to 425 and 657, to get

657 = 425 x 1 + 232

Step 3: We consider the new divisor 425 and the new remainder 232, and apply the division lemma to get

425 = 232 x 1 + 193

We consider the new divisor 232 and the new remainder 193,and apply the division lemma to get

232 = 193 x 1 + 39

We consider the new divisor 193 and the new remainder 39,and apply the division lemma to get

193 = 39 x 4 + 37

We consider the new divisor 39 and the new remainder 37,and apply the division lemma to get

39 = 37 x 1 + 2

We consider the new divisor 37 and the new remainder 2,and apply the division lemma to get

37 = 2 x 18 + 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 8966 and 657 is 1

Notice that 1 = HCF(2,1) = HCF(37,2) = HCF(39,37) = HCF(193,39) = HCF(232,193) = HCF(425,232) = HCF(657,425) = HCF(8966,657) .

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Frequently Asked Questions on HCF of 8966, 657 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 8966, 657?

Answer: HCF of 8966, 657 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 8966, 657 using Euclid's Algorithm?

Answer: For arbitrary numbers 8966, 657 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.