Highest Common Factor of 618, 981, 517 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 618, 981, 517 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 618, 981, 517 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 618, 981, 517 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 618, 981, 517 is 1.

HCF(618, 981, 517) = 1

HCF of 618, 981, 517 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 618, 981, 517 is 1.

Highest Common Factor of 618,981,517 using Euclid's algorithm

Highest Common Factor of 618,981,517 is 1

Step 1: Since 981 > 618, we apply the division lemma to 981 and 618, to get

981 = 618 x 1 + 363

Step 2: Since the reminder 618 ≠ 0, we apply division lemma to 363 and 618, to get

618 = 363 x 1 + 255

Step 3: We consider the new divisor 363 and the new remainder 255, and apply the division lemma to get

363 = 255 x 1 + 108

We consider the new divisor 255 and the new remainder 108,and apply the division lemma to get

255 = 108 x 2 + 39

We consider the new divisor 108 and the new remainder 39,and apply the division lemma to get

108 = 39 x 2 + 30

We consider the new divisor 39 and the new remainder 30,and apply the division lemma to get

39 = 30 x 1 + 9

We consider the new divisor 30 and the new remainder 9,and apply the division lemma to get

30 = 9 x 3 + 3

We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get

9 = 3 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 618 and 981 is 3

Notice that 3 = HCF(9,3) = HCF(30,9) = HCF(39,30) = HCF(108,39) = HCF(255,108) = HCF(363,255) = HCF(618,363) = HCF(981,618) .

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

Step 1: Since 517 > 3, we apply the division lemma to 517 and 3, to get

517 = 3 x 172 + 1

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, 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 3 and 517 is 1

Notice that 1 = HCF(3,1) = HCF(517,3) .

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Frequently Asked Questions on HCF of 618, 981, 517 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 618, 981, 517?

Answer: HCF of 618, 981, 517 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 618, 981, 517 using Euclid's Algorithm?

Answer: For arbitrary numbers 618, 981, 517 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.