Highest Common Factor of 891, 614, 772 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 891, 614, 772 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 891, 614, 772 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 891, 614, 772 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 891, 614, 772 is 1.

HCF(891, 614, 772) = 1

HCF of 891, 614, 772 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 891, 614, 772 is 1.

Highest Common Factor of 891,614,772 using Euclid's algorithm

Highest Common Factor of 891,614,772 is 1

Step 1: Since 891 > 614, we apply the division lemma to 891 and 614, to get

891 = 614 x 1 + 277

Step 2: Since the reminder 614 ≠ 0, we apply division lemma to 277 and 614, to get

614 = 277 x 2 + 60

Step 3: We consider the new divisor 277 and the new remainder 60, and apply the division lemma to get

277 = 60 x 4 + 37

We consider the new divisor 60 and the new remainder 37,and apply the division lemma to get

60 = 37 x 1 + 23

We consider the new divisor 37 and the new remainder 23,and apply the division lemma to get

37 = 23 x 1 + 14

We consider the new divisor 23 and the new remainder 14,and apply the division lemma to get

23 = 14 x 1 + 9

We consider the new divisor 14 and the new remainder 9,and apply the division lemma to get

14 = 9 x 1 + 5

We consider the new divisor 9 and the new remainder 5,and apply the division lemma to get

9 = 5 x 1 + 4

We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get

5 = 4 x 1 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 891 and 614 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(9,5) = HCF(14,9) = HCF(23,14) = HCF(37,23) = HCF(60,37) = HCF(277,60) = HCF(614,277) = HCF(891,614) .

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

Step 1: Since 772 > 1, we apply the division lemma to 772 and 1, to get

772 = 1 x 772 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 772 is 1

Notice that 1 = HCF(772,1) .

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Frequently Asked Questions on HCF of 891, 614, 772 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 891, 614, 772?

Answer: HCF of 891, 614, 772 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 891, 614, 772 using Euclid's Algorithm?

Answer: For arbitrary numbers 891, 614, 772 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.