Highest Common Factor of 706, 51951 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 706, 51951 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 706, 51951 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 706, 51951 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 706, 51951 is 1.

HCF(706, 51951) = 1

HCF of 706, 51951 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 706, 51951 is 1.

Highest Common Factor of 706,51951 using Euclid's algorithm

Highest Common Factor of 706,51951 is 1

Step 1: Since 51951 > 706, we apply the division lemma to 51951 and 706, to get

51951 = 706 x 73 + 413

Step 2: Since the reminder 706 ≠ 0, we apply division lemma to 413 and 706, to get

706 = 413 x 1 + 293

Step 3: We consider the new divisor 413 and the new remainder 293, and apply the division lemma to get

413 = 293 x 1 + 120

We consider the new divisor 293 and the new remainder 120,and apply the division lemma to get

293 = 120 x 2 + 53

We consider the new divisor 120 and the new remainder 53,and apply the division lemma to get

120 = 53 x 2 + 14

We consider the new divisor 53 and the new remainder 14,and apply the division lemma to get

53 = 14 x 3 + 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 706 and 51951 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(11,3) = HCF(14,11) = HCF(53,14) = HCF(120,53) = HCF(293,120) = HCF(413,293) = HCF(706,413) = HCF(51951,706) .

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Frequently Asked Questions on HCF of 706, 51951 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 706, 51951?

Answer: HCF of 706, 51951 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 706, 51951 using Euclid's Algorithm?

Answer: For arbitrary numbers 706, 51951 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.