Highest Common Factor of 851, 258, 638 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 851, 258, 638 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 851, 258, 638 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 851, 258, 638 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 851, 258, 638 is 1.

HCF(851, 258, 638) = 1

HCF of 851, 258, 638 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 851, 258, 638 is 1.

Highest Common Factor of 851,258,638 using Euclid's algorithm

Highest Common Factor of 851,258,638 is 1

Step 1: Since 851 > 258, we apply the division lemma to 851 and 258, to get

851 = 258 x 3 + 77

Step 2: Since the reminder 258 ≠ 0, we apply division lemma to 77 and 258, to get

258 = 77 x 3 + 27

Step 3: We consider the new divisor 77 and the new remainder 27, and apply the division lemma to get

77 = 27 x 2 + 23

We consider the new divisor 27 and the new remainder 23,and apply the division lemma to get

27 = 23 x 1 + 4

We consider the new divisor 23 and the new remainder 4,and apply the division lemma to get

23 = 4 x 5 + 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 851 and 258 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(23,4) = HCF(27,23) = HCF(77,27) = HCF(258,77) = HCF(851,258) .

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

Step 1: Since 638 > 1, we apply the division lemma to 638 and 1, to get

638 = 1 x 638 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 638 is 1

Notice that 1 = HCF(638,1) .

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Frequently Asked Questions on HCF of 851, 258, 638 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 851, 258, 638?

Answer: HCF of 851, 258, 638 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 851, 258, 638 using Euclid's Algorithm?

Answer: For arbitrary numbers 851, 258, 638 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.