Highest Common Factor of 291, 813, 872 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 291, 813, 872 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 291, 813, 872 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 291, 813, 872 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 291, 813, 872 is 1.

HCF(291, 813, 872) = 1

HCF of 291, 813, 872 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 291, 813, 872 is 1.

Highest Common Factor of 291,813,872 using Euclid's algorithm

Highest Common Factor of 291,813,872 is 1

Step 1: Since 813 > 291, we apply the division lemma to 813 and 291, to get

813 = 291 x 2 + 231

Step 2: Since the reminder 291 ≠ 0, we apply division lemma to 231 and 291, to get

291 = 231 x 1 + 60

Step 3: We consider the new divisor 231 and the new remainder 60, and apply the division lemma to get

231 = 60 x 3 + 51

We consider the new divisor 60 and the new remainder 51,and apply the division lemma to get

60 = 51 x 1 + 9

We consider the new divisor 51 and the new remainder 9,and apply the division lemma to get

51 = 9 x 5 + 6

We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get

9 = 6 x 1 + 3

We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get

6 = 3 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 291 and 813 is 3

Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(51,9) = HCF(60,51) = HCF(231,60) = HCF(291,231) = HCF(813,291) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Step 1: Since 872 > 3, we apply the division lemma to 872 and 3, to get

872 = 3 x 290 + 2

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get

3 = 2 x 1 + 1

Step 3: 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 3 and 872 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(872,3) .

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Frequently Asked Questions on HCF of 291, 813, 872 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 291, 813, 872?

Answer: HCF of 291, 813, 872 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 291, 813, 872 using Euclid's Algorithm?

Answer: For arbitrary numbers 291, 813, 872 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.