Highest Common Factor of 616, 747 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 616, 747 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 616, 747 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 616, 747 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 616, 747 is 1.

HCF(616, 747) = 1

HCF of 616, 747 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 616, 747 is 1.

Highest Common Factor of 616,747 using Euclid's algorithm

Highest Common Factor of 616,747 is 1

Step 1: Since 747 > 616, we apply the division lemma to 747 and 616, to get

747 = 616 x 1 + 131

Step 2: Since the reminder 616 ≠ 0, we apply division lemma to 131 and 616, to get

616 = 131 x 4 + 92

Step 3: We consider the new divisor 131 and the new remainder 92, and apply the division lemma to get

131 = 92 x 1 + 39

We consider the new divisor 92 and the new remainder 39,and apply the division lemma to get

92 = 39 x 2 + 14

We consider the new divisor 39 and the new remainder 14,and apply the division lemma to get

39 = 14 x 2 + 11

We consider the new divisor 14 and the new remainder 11,and apply the division lemma to get

14 = 11 x 1 + 3

We consider the new divisor 11 and the new remainder 3,and apply the division lemma to get

11 = 3 x 3 + 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 616 and 747 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(11,3) = HCF(14,11) = HCF(39,14) = HCF(92,39) = HCF(131,92) = HCF(616,131) = HCF(747,616) .

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Frequently Asked Questions on HCF of 616, 747 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 616, 747?

Answer: HCF of 616, 747 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 616, 747 using Euclid's Algorithm?

Answer: For arbitrary numbers 616, 747 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.