Highest Common Factor of 891, 9659 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, 9659 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 891, 9659 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, 9659 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, 9659 is 1.

HCF(891, 9659) = 1

HCF of 891, 9659 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, 9659 is 1.

Highest Common Factor of 891,9659 using Euclid's algorithm

Highest Common Factor of 891,9659 is 1

Step 1: Since 9659 > 891, we apply the division lemma to 9659 and 891, to get

9659 = 891 x 10 + 749

Step 2: Since the reminder 891 ≠ 0, we apply division lemma to 749 and 891, to get

891 = 749 x 1 + 142

Step 3: We consider the new divisor 749 and the new remainder 142, and apply the division lemma to get

749 = 142 x 5 + 39

We consider the new divisor 142 and the new remainder 39,and apply the division lemma to get

142 = 39 x 3 + 25

We consider the new divisor 39 and the new remainder 25,and apply the division lemma to get

39 = 25 x 1 + 14

We consider the new divisor 25 and the new remainder 14,and apply the division lemma to get

25 = 14 x 1 + 11

We consider the new divisor 14 and the new remainder 11,and apply the division lemma to get

14 = 11 x 1 + 3

We consider the new divisor 11 and the new remainder 3,and apply the division lemma to get

11 = 3 x 3 + 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 9659 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(11,3) = HCF(14,11) = HCF(25,14) = HCF(39,25) = HCF(142,39) = HCF(749,142) = HCF(891,749) = HCF(9659,891) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 891, 9659 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, 9659?

Answer: HCF of 891, 9659 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 891, 9659 using Euclid's Algorithm?

Answer: For arbitrary numbers 891, 9659 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.