Highest Common Factor of 517, 925, 676 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 517, 925, 676 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 517, 925, 676 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 517, 925, 676 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 517, 925, 676 is 1.

HCF(517, 925, 676) = 1

HCF of 517, 925, 676 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 517, 925, 676 is 1.

Highest Common Factor of 517,925,676 using Euclid's algorithm

Highest Common Factor of 517,925,676 is 1

Step 1: Since 925 > 517, we apply the division lemma to 925 and 517, to get

925 = 517 x 1 + 408

Step 2: Since the reminder 517 ≠ 0, we apply division lemma to 408 and 517, to get

517 = 408 x 1 + 109

Step 3: We consider the new divisor 408 and the new remainder 109, and apply the division lemma to get

408 = 109 x 3 + 81

We consider the new divisor 109 and the new remainder 81,and apply the division lemma to get

109 = 81 x 1 + 28

We consider the new divisor 81 and the new remainder 28,and apply the division lemma to get

81 = 28 x 2 + 25

We consider the new divisor 28 and the new remainder 25,and apply the division lemma to get

28 = 25 x 1 + 3

We consider the new divisor 25 and the new remainder 3,and apply the division lemma to get

25 = 3 x 8 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 517 and 925 is 1

Notice that 1 = HCF(3,1) = HCF(25,3) = HCF(28,25) = HCF(81,28) = HCF(109,81) = HCF(408,109) = HCF(517,408) = HCF(925,517) .

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

Step 1: Since 676 > 1, we apply the division lemma to 676 and 1, to get

676 = 1 x 676 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 676 is 1

Notice that 1 = HCF(676,1) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 517, 925, 676 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 517, 925, 676?

Answer: HCF of 517, 925, 676 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 517, 925, 676 using Euclid's Algorithm?

Answer: For arbitrary numbers 517, 925, 676 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.