Highest Common Factor of 512, 808, 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 512, 808, 657 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 512, 808, 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 512, 808, 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 512, 808, 657 is 1.

HCF(512, 808, 657) = 1

HCF of 512, 808, 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 512, 808, 657 is 1.

Highest Common Factor of 512,808,657 using Euclid's algorithm

Highest Common Factor of 512,808,657 is 1

Step 1: Since 808 > 512, we apply the division lemma to 808 and 512, to get

808 = 512 x 1 + 296

Step 2: Since the reminder 512 ≠ 0, we apply division lemma to 296 and 512, to get

512 = 296 x 1 + 216

Step 3: We consider the new divisor 296 and the new remainder 216, and apply the division lemma to get

296 = 216 x 1 + 80

We consider the new divisor 216 and the new remainder 80,and apply the division lemma to get

216 = 80 x 2 + 56

We consider the new divisor 80 and the new remainder 56,and apply the division lemma to get

80 = 56 x 1 + 24

We consider the new divisor 56 and the new remainder 24,and apply the division lemma to get

56 = 24 x 2 + 8

We consider the new divisor 24 and the new remainder 8,and apply the division lemma to get

24 = 8 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 512 and 808 is 8

Notice that 8 = HCF(24,8) = HCF(56,24) = HCF(80,56) = HCF(216,80) = HCF(296,216) = HCF(512,296) = HCF(808,512) .

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

Step 1: Since 657 > 8, we apply the division lemma to 657 and 8, to get

657 = 8 x 82 + 1

Step 2: Since the reminder 8 ≠ 0, we apply division lemma to 1 and 8, to get

8 = 1 x 8 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 8 and 657 is 1

Notice that 1 = HCF(8,1) = HCF(657,8) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 512, 808, 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 512, 808, 657?

Answer: HCF of 512, 808, 657 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 512, 808, 657 using Euclid's Algorithm?

Answer: For arbitrary numbers 512, 808, 657 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.