Highest Common Factor of 9759, 8740 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 9759, 8740 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 9759, 8740 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 9759, 8740 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 9759, 8740 is 1.

HCF(9759, 8740) = 1

HCF of 9759, 8740 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 9759, 8740 is 1.

Highest Common Factor of 9759,8740 using Euclid's algorithm

Highest Common Factor of 9759,8740 is 1

Step 1: Since 9759 > 8740, we apply the division lemma to 9759 and 8740, to get

9759 = 8740 x 1 + 1019

Step 2: Since the reminder 8740 ≠ 0, we apply division lemma to 1019 and 8740, to get

8740 = 1019 x 8 + 588

Step 3: We consider the new divisor 1019 and the new remainder 588, and apply the division lemma to get

1019 = 588 x 1 + 431

We consider the new divisor 588 and the new remainder 431,and apply the division lemma to get

588 = 431 x 1 + 157

We consider the new divisor 431 and the new remainder 157,and apply the division lemma to get

431 = 157 x 2 + 117

We consider the new divisor 157 and the new remainder 117,and apply the division lemma to get

157 = 117 x 1 + 40

We consider the new divisor 117 and the new remainder 40,and apply the division lemma to get

117 = 40 x 2 + 37

We consider the new divisor 40 and the new remainder 37,and apply the division lemma to get

40 = 37 x 1 + 3

We consider the new divisor 37 and the new remainder 3,and apply the division lemma to get

37 = 3 x 12 + 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 9759 and 8740 is 1

Notice that 1 = HCF(3,1) = HCF(37,3) = HCF(40,37) = HCF(117,40) = HCF(157,117) = HCF(431,157) = HCF(588,431) = HCF(1019,588) = HCF(8740,1019) = HCF(9759,8740) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 9759, 8740 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 9759, 8740?

Answer: HCF of 9759, 8740 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 9759, 8740 using Euclid's Algorithm?

Answer: For arbitrary numbers 9759, 8740 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.