Highest Common Factor of 517, 299, 916, 637 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, 299, 916, 637 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 517, 299, 916, 637 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, 299, 916, 637 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, 299, 916, 637 is 1.

HCF(517, 299, 916, 637) = 1

HCF of 517, 299, 916, 637 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, 299, 916, 637 is 1.

Highest Common Factor of 517,299,916,637 using Euclid's algorithm

Highest Common Factor of 517,299,916,637 is 1

Step 1: Since 517 > 299, we apply the division lemma to 517 and 299, to get

517 = 299 x 1 + 218

Step 2: Since the reminder 299 ≠ 0, we apply division lemma to 218 and 299, to get

299 = 218 x 1 + 81

Step 3: We consider the new divisor 218 and the new remainder 81, and apply the division lemma to get

218 = 81 x 2 + 56

We consider the new divisor 81 and the new remainder 56,and apply the division lemma to get

81 = 56 x 1 + 25

We consider the new divisor 56 and the new remainder 25,and apply the division lemma to get

56 = 25 x 2 + 6

We consider the new divisor 25 and the new remainder 6,and apply the division lemma to get

25 = 6 x 4 + 1

We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get

6 = 1 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 517 and 299 is 1

Notice that 1 = HCF(6,1) = HCF(25,6) = HCF(56,25) = HCF(81,56) = HCF(218,81) = HCF(299,218) = HCF(517,299) .

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

Step 1: Since 916 > 1, we apply the division lemma to 916 and 1, to get

916 = 1 x 916 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 916 is 1

Notice that 1 = HCF(916,1) .

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

Step 1: Since 637 > 1, we apply the division lemma to 637 and 1, to get

637 = 1 x 637 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 637 is 1

Notice that 1 = HCF(637,1) .

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, 299, 916, 637 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, 299, 916, 637?

Answer: HCF of 517, 299, 916, 637 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 517, 299, 916, 637 using Euclid's Algorithm?

Answer: For arbitrary numbers 517, 299, 916, 637 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.