Highest Common Factor of 706, 537 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, 537 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 706, 537 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, 537 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, 537 is 1.

HCF(706, 537) = 1

HCF of 706, 537 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, 537 is 1.

Highest Common Factor of 706,537 using Euclid's algorithm

Highest Common Factor of 706,537 is 1

Step 1: Since 706 > 537, we apply the division lemma to 706 and 537, to get

706 = 537 x 1 + 169

Step 2: Since the reminder 537 ≠ 0, we apply division lemma to 169 and 537, to get

537 = 169 x 3 + 30

Step 3: We consider the new divisor 169 and the new remainder 30, and apply the division lemma to get

169 = 30 x 5 + 19

We consider the new divisor 30 and the new remainder 19,and apply the division lemma to get

30 = 19 x 1 + 11

We consider the new divisor 19 and the new remainder 11,and apply the division lemma to get

19 = 11 x 1 + 8

We consider the new divisor 11 and the new remainder 8,and apply the division lemma to get

11 = 8 x 1 + 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 706 and 537 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(8,3) = HCF(11,8) = HCF(19,11) = HCF(30,19) = HCF(169,30) = HCF(537,169) = HCF(706,537) .

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Frequently Asked Questions on HCF of 706, 537 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, 537?

Answer: HCF of 706, 537 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 706, 537 using Euclid's Algorithm?

Answer: For arbitrary numbers 706, 537 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.