Highest Common Factor of 2072, 615 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 2072, 615 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 2072, 615 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 2072, 615 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 2072, 615 is 1.

HCF(2072, 615) = 1

HCF of 2072, 615 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 2072, 615 is 1.

Highest Common Factor of 2072,615 using Euclid's algorithm

Highest Common Factor of 2072,615 is 1

Step 1: Since 2072 > 615, we apply the division lemma to 2072 and 615, to get

2072 = 615 x 3 + 227

Step 2: Since the reminder 615 ≠ 0, we apply division lemma to 227 and 615, to get

615 = 227 x 2 + 161

Step 3: We consider the new divisor 227 and the new remainder 161, and apply the division lemma to get

227 = 161 x 1 + 66

We consider the new divisor 161 and the new remainder 66,and apply the division lemma to get

161 = 66 x 2 + 29

We consider the new divisor 66 and the new remainder 29,and apply the division lemma to get

66 = 29 x 2 + 8

We consider the new divisor 29 and the new remainder 8,and apply the division lemma to get

29 = 8 x 3 + 5

We consider the new divisor 8 and the new remainder 5,and apply the division lemma to get

8 = 5 x 1 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 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 2072 and 615 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(29,8) = HCF(66,29) = HCF(161,66) = HCF(227,161) = HCF(615,227) = HCF(2072,615) .

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Frequently Asked Questions on HCF of 2072, 615 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 2072, 615?

Answer: HCF of 2072, 615 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 2072, 615 using Euclid's Algorithm?

Answer: For arbitrary numbers 2072, 615 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.