Highest Common Factor of 872, 627, 607 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, 627, 607 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 872, 627, 607 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, 627, 607 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, 627, 607 is 1.

HCF(872, 627, 607) = 1

HCF of 872, 627, 607 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, 627, 607 is 1.

Highest Common Factor of 872,627,607 using Euclid's algorithm

Highest Common Factor of 872,627,607 is 1

Step 1: Since 872 > 627, we apply the division lemma to 872 and 627, to get

872 = 627 x 1 + 245

Step 2: Since the reminder 627 ≠ 0, we apply division lemma to 245 and 627, to get

627 = 245 x 2 + 137

Step 3: We consider the new divisor 245 and the new remainder 137, and apply the division lemma to get

245 = 137 x 1 + 108

We consider the new divisor 137 and the new remainder 108,and apply the division lemma to get

137 = 108 x 1 + 29

We consider the new divisor 108 and the new remainder 29,and apply the division lemma to get

108 = 29 x 3 + 21

We consider the new divisor 29 and the new remainder 21,and apply the division lemma to get

29 = 21 x 1 + 8

We consider the new divisor 21 and the new remainder 8,and apply the division lemma to get

21 = 8 x 2 + 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 872 and 627 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(21,8) = HCF(29,21) = HCF(108,29) = HCF(137,108) = HCF(245,137) = HCF(627,245) = HCF(872,627) .

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

Step 1: Since 607 > 1, we apply the division lemma to 607 and 1, to get

607 = 1 x 607 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 607 is 1

Notice that 1 = HCF(607,1) .

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Frequently Asked Questions on HCF of 872, 627, 607 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, 627, 607?

Answer: HCF of 872, 627, 607 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 872, 627, 607 using Euclid's Algorithm?

Answer: For arbitrary numbers 872, 627, 607 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.