Highest Common Factor of 6946, 9523 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 6946, 9523 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 6946, 9523 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 6946, 9523 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 6946, 9523 is 1.

HCF(6946, 9523) = 1

HCF of 6946, 9523 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

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Highest common factor (HCF) of 6946, 9523 is 1.

Highest Common Factor of 6946,9523 using Euclid's algorithm

Highest Common Factor of 6946,9523 is 1

Step 1: Since 9523 > 6946, we apply the division lemma to 9523 and 6946, to get

9523 = 6946 x 1 + 2577

Step 2: Since the reminder 6946 ≠ 0, we apply division lemma to 2577 and 6946, to get

6946 = 2577 x 2 + 1792

Step 3: We consider the new divisor 2577 and the new remainder 1792, and apply the division lemma to get

2577 = 1792 x 1 + 785

We consider the new divisor 1792 and the new remainder 785,and apply the division lemma to get

1792 = 785 x 2 + 222

We consider the new divisor 785 and the new remainder 222,and apply the division lemma to get

785 = 222 x 3 + 119

We consider the new divisor 222 and the new remainder 119,and apply the division lemma to get

222 = 119 x 1 + 103

We consider the new divisor 119 and the new remainder 103,and apply the division lemma to get

119 = 103 x 1 + 16

We consider the new divisor 103 and the new remainder 16,and apply the division lemma to get

103 = 16 x 6 + 7

We consider the new divisor 16 and the new remainder 7,and apply the division lemma to get

16 = 7 x 2 + 2

We consider the new divisor 7 and the new remainder 2,and apply the division lemma to get

7 = 2 x 3 + 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 6946 and 9523 is 1

Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(16,7) = HCF(103,16) = HCF(119,103) = HCF(222,119) = HCF(785,222) = HCF(1792,785) = HCF(2577,1792) = HCF(6946,2577) = HCF(9523,6946) .

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Frequently Asked Questions on HCF of 6946, 9523 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 6946, 9523?

Answer: HCF of 6946, 9523 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 6946, 9523 using Euclid's Algorithm?

Answer: For arbitrary numbers 6946, 9523 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.