Highest Common Factor of 657, 518, 470 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 657, 518, 470 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 657, 518, 470 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 657, 518, 470 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 657, 518, 470 is 1.

HCF(657, 518, 470) = 1

HCF of 657, 518, 470 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 657, 518, 470 is 1.

Highest Common Factor of 657,518,470 using Euclid's algorithm

Highest Common Factor of 657,518,470 is 1

Step 1: Since 657 > 518, we apply the division lemma to 657 and 518, to get

657 = 518 x 1 + 139

Step 2: Since the reminder 518 ≠ 0, we apply division lemma to 139 and 518, to get

518 = 139 x 3 + 101

Step 3: We consider the new divisor 139 and the new remainder 101, and apply the division lemma to get

139 = 101 x 1 + 38

We consider the new divisor 101 and the new remainder 38,and apply the division lemma to get

101 = 38 x 2 + 25

We consider the new divisor 38 and the new remainder 25,and apply the division lemma to get

38 = 25 x 1 + 13

We consider the new divisor 25 and the new remainder 13,and apply the division lemma to get

25 = 13 x 1 + 12

We consider the new divisor 13 and the new remainder 12,and apply the division lemma to get

13 = 12 x 1 + 1

We consider the new divisor 12 and the new remainder 1,and apply the division lemma to get

12 = 1 x 12 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 657 and 518 is 1

Notice that 1 = HCF(12,1) = HCF(13,12) = HCF(25,13) = HCF(38,25) = HCF(101,38) = HCF(139,101) = HCF(518,139) = HCF(657,518) .

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

Step 1: Since 470 > 1, we apply the division lemma to 470 and 1, to get

470 = 1 x 470 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 470 is 1

Notice that 1 = HCF(470,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 657, 518, 470 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 657, 518, 470?

Answer: HCF of 657, 518, 470 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 657, 518, 470 using Euclid's Algorithm?

Answer: For arbitrary numbers 657, 518, 470 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.