Highest Common Factor of 872, 541 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 872, 541 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 872, 541 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 872, 541 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 872, 541 is 1.

HCF(872, 541) = 1

HCF of 872, 541 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 872, 541 is 1.

Highest Common Factor of 872,541 using Euclid's algorithm

Highest Common Factor of 872,541 is 1

Step 1: Since 872 > 541, we apply the division lemma to 872 and 541, to get

872 = 541 x 1 + 331

Step 2: Since the reminder 541 ≠ 0, we apply division lemma to 331 and 541, to get

541 = 331 x 1 + 210

Step 3: We consider the new divisor 331 and the new remainder 210, and apply the division lemma to get

331 = 210 x 1 + 121

We consider the new divisor 210 and the new remainder 121,and apply the division lemma to get

210 = 121 x 1 + 89

We consider the new divisor 121 and the new remainder 89,and apply the division lemma to get

121 = 89 x 1 + 32

We consider the new divisor 89 and the new remainder 32,and apply the division lemma to get

89 = 32 x 2 + 25

We consider the new divisor 32 and the new remainder 25,and apply the division lemma to get

32 = 25 x 1 + 7

We consider the new divisor 25 and the new remainder 7,and apply the division lemma to get

25 = 7 x 3 + 4

We consider the new divisor 7 and the new remainder 4,and apply the division lemma to get

7 = 4 x 1 + 3

We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get

4 = 3 x 1 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 872 and 541 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(7,4) = HCF(25,7) = HCF(32,25) = HCF(89,32) = HCF(121,89) = HCF(210,121) = HCF(331,210) = HCF(541,331) = HCF(872,541) .

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Frequently Asked Questions on HCF of 872, 541 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 872, 541?

Answer: HCF of 872, 541 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 872, 541 using Euclid's Algorithm?

Answer: For arbitrary numbers 872, 541 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.