Highest Common Factor of 517, 297, 57 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, 297, 57 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 517, 297, 57 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, 297, 57 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, 297, 57 is 1.

HCF(517, 297, 57) = 1

HCF of 517, 297, 57 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, 297, 57 is 1.

Highest Common Factor of 517,297,57 using Euclid's algorithm

Highest Common Factor of 517,297,57 is 1

Step 1: Since 517 > 297, we apply the division lemma to 517 and 297, to get

517 = 297 x 1 + 220

Step 2: Since the reminder 297 ≠ 0, we apply division lemma to 220 and 297, to get

297 = 220 x 1 + 77

Step 3: We consider the new divisor 220 and the new remainder 77, and apply the division lemma to get

220 = 77 x 2 + 66

We consider the new divisor 77 and the new remainder 66,and apply the division lemma to get

77 = 66 x 1 + 11

We consider the new divisor 66 and the new remainder 11,and apply the division lemma to get

66 = 11 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 11, the HCF of 517 and 297 is 11

Notice that 11 = HCF(66,11) = HCF(77,66) = HCF(220,77) = HCF(297,220) = HCF(517,297) .

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

Step 1: Since 57 > 11, we apply the division lemma to 57 and 11, to get

57 = 11 x 5 + 2

Step 2: Since the reminder 11 ≠ 0, we apply division lemma to 2 and 11, to get

11 = 2 x 5 + 1

Step 3: We consider the new divisor 2 and the new remainder 1, and apply the division lemma to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 11 and 57 is 1

Notice that 1 = HCF(2,1) = HCF(11,2) = HCF(57,11) .

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, 297, 57 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, 297, 57?

Answer: HCF of 517, 297, 57 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 517, 297, 57 using Euclid's Algorithm?

Answer: For arbitrary numbers 517, 297, 57 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.