Highest Common Factor of 517, 986, 645 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, 986, 645 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 517, 986, 645 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, 986, 645 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, 986, 645 is 1.

HCF(517, 986, 645) = 1

HCF of 517, 986, 645 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, 986, 645 is 1.

Highest Common Factor of 517,986,645 using Euclid's algorithm

Highest Common Factor of 517,986,645 is 1

Step 1: Since 986 > 517, we apply the division lemma to 986 and 517, to get

986 = 517 x 1 + 469

Step 2: Since the reminder 517 ≠ 0, we apply division lemma to 469 and 517, to get

517 = 469 x 1 + 48

Step 3: We consider the new divisor 469 and the new remainder 48, and apply the division lemma to get

469 = 48 x 9 + 37

We consider the new divisor 48 and the new remainder 37,and apply the division lemma to get

48 = 37 x 1 + 11

We consider the new divisor 37 and the new remainder 11,and apply the division lemma to get

37 = 11 x 3 + 4

We consider the new divisor 11 and the new remainder 4,and apply the division lemma to get

11 = 4 x 2 + 3

We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get

4 = 3 x 1 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma 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 517 and 986 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(11,4) = HCF(37,11) = HCF(48,37) = HCF(469,48) = HCF(517,469) = HCF(986,517) .

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

Step 1: Since 645 > 1, we apply the division lemma to 645 and 1, to get

645 = 1 x 645 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 645 is 1

Notice that 1 = HCF(645,1) .

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Frequently Asked Questions on HCF of 517, 986, 645 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, 986, 645?

Answer: HCF of 517, 986, 645 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 517, 986, 645 using Euclid's Algorithm?

Answer: For arbitrary numbers 517, 986, 645 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.