Highest Common Factor of 516, 697, 462 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 516, 697, 462 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 516, 697, 462 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 516, 697, 462 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 516, 697, 462 is 1.

HCF(516, 697, 462) = 1

HCF of 516, 697, 462 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 516, 697, 462 is 1.

Highest Common Factor of 516,697,462 using Euclid's algorithm

Highest Common Factor of 516,697,462 is 1

Step 1: Since 697 > 516, we apply the division lemma to 697 and 516, to get

697 = 516 x 1 + 181

Step 2: Since the reminder 516 ≠ 0, we apply division lemma to 181 and 516, to get

516 = 181 x 2 + 154

Step 3: We consider the new divisor 181 and the new remainder 154, and apply the division lemma to get

181 = 154 x 1 + 27

We consider the new divisor 154 and the new remainder 27,and apply the division lemma to get

154 = 27 x 5 + 19

We consider the new divisor 27 and the new remainder 19,and apply the division lemma to get

27 = 19 x 1 + 8

We consider the new divisor 19 and the new remainder 8,and apply the division lemma to get

19 = 8 x 2 + 3

We consider the new divisor 8 and the new remainder 3,and apply the division lemma to get

8 = 3 x 2 + 2

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

3 = 2 x 1 + 1

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 516 and 697 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(8,3) = HCF(19,8) = HCF(27,19) = HCF(154,27) = HCF(181,154) = HCF(516,181) = HCF(697,516) .

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

Step 1: Since 462 > 1, we apply the division lemma to 462 and 1, to get

462 = 1 x 462 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 462 is 1

Notice that 1 = HCF(462,1) .

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Frequently Asked Questions on HCF of 516, 697, 462 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 516, 697, 462?

Answer: HCF of 516, 697, 462 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 516, 697, 462 using Euclid's Algorithm?

Answer: For arbitrary numbers 516, 697, 462 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.