Highest Common Factor of 891, 7687 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, 7687 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 891, 7687 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, 7687 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, 7687 is 1.

HCF(891, 7687) = 1

HCF of 891, 7687 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, 7687 is 1.

Highest Common Factor of 891,7687 using Euclid's algorithm

Highest Common Factor of 891,7687 is 1

Step 1: Since 7687 > 891, we apply the division lemma to 7687 and 891, to get

7687 = 891 x 8 + 559

Step 2: Since the reminder 891 ≠ 0, we apply division lemma to 559 and 891, to get

891 = 559 x 1 + 332

Step 3: We consider the new divisor 559 and the new remainder 332, and apply the division lemma to get

559 = 332 x 1 + 227

We consider the new divisor 332 and the new remainder 227,and apply the division lemma to get

332 = 227 x 1 + 105

We consider the new divisor 227 and the new remainder 105,and apply the division lemma to get

227 = 105 x 2 + 17

We consider the new divisor 105 and the new remainder 17,and apply the division lemma to get

105 = 17 x 6 + 3

We consider the new divisor 17 and the new remainder 3,and apply the division lemma to get

17 = 3 x 5 + 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 891 and 7687 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(17,3) = HCF(105,17) = HCF(227,105) = HCF(332,227) = HCF(559,332) = HCF(891,559) = HCF(7687,891) .

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Frequently Asked Questions on HCF of 891, 7687 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, 7687?

Answer: HCF of 891, 7687 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 891, 7687 using Euclid's Algorithm?

Answer: For arbitrary numbers 891, 7687 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.