Highest Common Factor of 972, 841 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 972, 841 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 972, 841 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 972, 841 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 972, 841 is 1.

HCF(972, 841) = 1

HCF of 972, 841 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 972, 841 is 1.

Highest Common Factor of 972,841 using Euclid's algorithm

Highest Common Factor of 972,841 is 1

Step 1: Since 972 > 841, we apply the division lemma to 972 and 841, to get

972 = 841 x 1 + 131

Step 2: Since the reminder 841 ≠ 0, we apply division lemma to 131 and 841, to get

841 = 131 x 6 + 55

Step 3: We consider the new divisor 131 and the new remainder 55, and apply the division lemma to get

131 = 55 x 2 + 21

We consider the new divisor 55 and the new remainder 21,and apply the division lemma to get

55 = 21 x 2 + 13

We consider the new divisor 21 and the new remainder 13,and apply the division lemma to get

21 = 13 x 1 + 8

We consider the new divisor 13 and the new remainder 8,and apply the division lemma to get

13 = 8 x 1 + 5

We consider the new divisor 8 and the new remainder 5,and apply the division lemma to get

8 = 5 x 1 + 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 972 and 841 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(13,8) = HCF(21,13) = HCF(55,21) = HCF(131,55) = HCF(841,131) = HCF(972,841) .

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Frequently Asked Questions on HCF of 972, 841 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 972, 841?

Answer: HCF of 972, 841 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 972, 841 using Euclid's Algorithm?

Answer: For arbitrary numbers 972, 841 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.