Highest Common Factor of 712, 979, 562 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 712, 979, 562 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 712, 979, 562 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 712, 979, 562 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 712, 979, 562 is 1.

HCF(712, 979, 562) = 1

HCF of 712, 979, 562 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 712, 979, 562 is 1.

Highest Common Factor of 712,979,562 using Euclid's algorithm

Highest Common Factor of 712,979,562 is 1

Step 1: Since 979 > 712, we apply the division lemma to 979 and 712, to get

979 = 712 x 1 + 267

Step 2: Since the reminder 712 ≠ 0, we apply division lemma to 267 and 712, to get

712 = 267 x 2 + 178

Step 3: We consider the new divisor 267 and the new remainder 178, and apply the division lemma to get

267 = 178 x 1 + 89

We consider the new divisor 178 and the new remainder 89, and apply the division lemma to get

178 = 89 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 89, the HCF of 712 and 979 is 89

Notice that 89 = HCF(178,89) = HCF(267,178) = HCF(712,267) = HCF(979,712) .

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

Step 1: Since 562 > 89, we apply the division lemma to 562 and 89, to get

562 = 89 x 6 + 28

Step 2: Since the reminder 89 ≠ 0, we apply division lemma to 28 and 89, to get

89 = 28 x 3 + 5

Step 3: We consider the new divisor 28 and the new remainder 5, and apply the division lemma to get

28 = 5 x 5 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 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 89 and 562 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(28,5) = HCF(89,28) = HCF(562,89) .

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Frequently Asked Questions on HCF of 712, 979, 562 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 712, 979, 562?

Answer: HCF of 712, 979, 562 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 712, 979, 562 using Euclid's Algorithm?

Answer: For arbitrary numbers 712, 979, 562 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.