Highest Common Factor of 877, 645, 765 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 877, 645, 765 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 877, 645, 765 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 877, 645, 765 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 877, 645, 765 is 1.

HCF(877, 645, 765) = 1

HCF of 877, 645, 765 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 877, 645, 765 is 1.

Highest Common Factor of 877,645,765 using Euclid's algorithm

Highest Common Factor of 877,645,765 is 1

Step 1: Since 877 > 645, we apply the division lemma to 877 and 645, to get

877 = 645 x 1 + 232

Step 2: Since the reminder 645 ≠ 0, we apply division lemma to 232 and 645, to get

645 = 232 x 2 + 181

Step 3: We consider the new divisor 232 and the new remainder 181, and apply the division lemma to get

232 = 181 x 1 + 51

We consider the new divisor 181 and the new remainder 51,and apply the division lemma to get

181 = 51 x 3 + 28

We consider the new divisor 51 and the new remainder 28,and apply the division lemma to get

51 = 28 x 1 + 23

We consider the new divisor 28 and the new remainder 23,and apply the division lemma to get

28 = 23 x 1 + 5

We consider the new divisor 23 and the new remainder 5,and apply the division lemma to get

23 = 5 x 4 + 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 877 and 645 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(23,5) = HCF(28,23) = HCF(51,28) = HCF(181,51) = HCF(232,181) = HCF(645,232) = HCF(877,645) .

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

Step 1: Since 765 > 1, we apply the division lemma to 765 and 1, to get

765 = 1 x 765 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 765 is 1

Notice that 1 = HCF(765,1) .

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Frequently Asked Questions on HCF of 877, 645, 765 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 877, 645, 765?

Answer: HCF of 877, 645, 765 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 877, 645, 765 using Euclid's Algorithm?

Answer: For arbitrary numbers 877, 645, 765 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.