Highest Common Factor of 2740, 9680, 83659 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 2740, 9680, 83659 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 2740, 9680, 83659 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 2740, 9680, 83659 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 2740, 9680, 83659 is 1.

HCF(2740, 9680, 83659) = 1

HCF of 2740, 9680, 83659 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 2740, 9680, 83659 is 1.

Highest Common Factor of 2740,9680,83659 using Euclid's algorithm

Highest Common Factor of 2740,9680,83659 is 1

Step 1: Since 9680 > 2740, we apply the division lemma to 9680 and 2740, to get

9680 = 2740 x 3 + 1460

Step 2: Since the reminder 2740 ≠ 0, we apply division lemma to 1460 and 2740, to get

2740 = 1460 x 1 + 1280

Step 3: We consider the new divisor 1460 and the new remainder 1280, and apply the division lemma to get

1460 = 1280 x 1 + 180

We consider the new divisor 1280 and the new remainder 180,and apply the division lemma to get

1280 = 180 x 7 + 20

We consider the new divisor 180 and the new remainder 20,and apply the division lemma to get

180 = 20 x 9 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 20, the HCF of 2740 and 9680 is 20

Notice that 20 = HCF(180,20) = HCF(1280,180) = HCF(1460,1280) = HCF(2740,1460) = HCF(9680,2740) .

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

Step 1: Since 83659 > 20, we apply the division lemma to 83659 and 20, to get

83659 = 20 x 4182 + 19

Step 2: Since the reminder 20 ≠ 0, we apply division lemma to 19 and 20, to get

20 = 19 x 1 + 1

Step 3: We consider the new divisor 19 and the new remainder 1, and apply the division lemma to get

19 = 1 x 19 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 20 and 83659 is 1

Notice that 1 = HCF(19,1) = HCF(20,19) = HCF(83659,20) .

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Frequently Asked Questions on HCF of 2740, 9680, 83659 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 2740, 9680, 83659?

Answer: HCF of 2740, 9680, 83659 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 2740, 9680, 83659 using Euclid's Algorithm?

Answer: For arbitrary numbers 2740, 9680, 83659 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.