Highest Common Factor of 876, 645, 251 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 876, 645, 251 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 876, 645, 251 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 876, 645, 251 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 876, 645, 251 is 1.

HCF(876, 645, 251) = 1

HCF of 876, 645, 251 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 876, 645, 251 is 1.

Highest Common Factor of 876,645,251 using Euclid's algorithm

Highest Common Factor of 876,645,251 is 1

Step 1: Since 876 > 645, we apply the division lemma to 876 and 645, to get

876 = 645 x 1 + 231

Step 2: Since the reminder 645 ≠ 0, we apply division lemma to 231 and 645, to get

645 = 231 x 2 + 183

Step 3: We consider the new divisor 231 and the new remainder 183, and apply the division lemma to get

231 = 183 x 1 + 48

We consider the new divisor 183 and the new remainder 48,and apply the division lemma to get

183 = 48 x 3 + 39

We consider the new divisor 48 and the new remainder 39,and apply the division lemma to get

48 = 39 x 1 + 9

We consider the new divisor 39 and the new remainder 9,and apply the division lemma to get

39 = 9 x 4 + 3

We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get

9 = 3 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 876 and 645 is 3

Notice that 3 = HCF(9,3) = HCF(39,9) = HCF(48,39) = HCF(183,48) = HCF(231,183) = HCF(645,231) = HCF(876,645) .

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

Step 1: Since 251 > 3, we apply the division lemma to 251 and 3, to get

251 = 3 x 83 + 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 251 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(251,3) .

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Frequently Asked Questions on HCF of 876, 645, 251 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 876, 645, 251?

Answer: HCF of 876, 645, 251 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 876, 645, 251 using Euclid's Algorithm?

Answer: For arbitrary numbers 876, 645, 251 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.