Highest Common Factor of 677, 531, 64 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 677, 531, 64 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 677, 531, 64 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 677, 531, 64 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 677, 531, 64 is 1.

HCF(677, 531, 64) = 1

HCF of 677, 531, 64 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 677, 531, 64 is 1.

Highest Common Factor of 677,531,64 using Euclid's algorithm

Highest Common Factor of 677,531,64 is 1

Step 1: Since 677 > 531, we apply the division lemma to 677 and 531, to get

677 = 531 x 1 + 146

Step 2: Since the reminder 531 ≠ 0, we apply division lemma to 146 and 531, to get

531 = 146 x 3 + 93

Step 3: We consider the new divisor 146 and the new remainder 93, and apply the division lemma to get

146 = 93 x 1 + 53

We consider the new divisor 93 and the new remainder 53,and apply the division lemma to get

93 = 53 x 1 + 40

We consider the new divisor 53 and the new remainder 40,and apply the division lemma to get

53 = 40 x 1 + 13

We consider the new divisor 40 and the new remainder 13,and apply the division lemma to get

40 = 13 x 3 + 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 677 and 531 is 1

Notice that 1 = HCF(13,1) = HCF(40,13) = HCF(53,40) = HCF(93,53) = HCF(146,93) = HCF(531,146) = HCF(677,531) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Step 1: Since 64 > 1, we apply the division lemma to 64 and 1, to get

64 = 1 x 64 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 64 is 1

Notice that 1 = HCF(64,1) .

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Frequently Asked Questions on HCF of 677, 531, 64 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 677, 531, 64?

Answer: HCF of 677, 531, 64 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 677, 531, 64 using Euclid's Algorithm?

Answer: For arbitrary numbers 677, 531, 64 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.