Highest Common Factor of 3617, 421 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 3617, 421 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 3617, 421 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 3617, 421 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 3617, 421 is 1.

HCF(3617, 421) = 1

HCF of 3617, 421 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 3617, 421 is 1.

Highest Common Factor of 3617,421 using Euclid's algorithm

Highest Common Factor of 3617,421 is 1

Step 1: Since 3617 > 421, we apply the division lemma to 3617 and 421, to get

3617 = 421 x 8 + 249

Step 2: Since the reminder 421 ≠ 0, we apply division lemma to 249 and 421, to get

421 = 249 x 1 + 172

Step 3: We consider the new divisor 249 and the new remainder 172, and apply the division lemma to get

249 = 172 x 1 + 77

We consider the new divisor 172 and the new remainder 77,and apply the division lemma to get

172 = 77 x 2 + 18

We consider the new divisor 77 and the new remainder 18,and apply the division lemma to get

77 = 18 x 4 + 5

We consider the new divisor 18 and the new remainder 5,and apply the division lemma to get

18 = 5 x 3 + 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 3617 and 421 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(18,5) = HCF(77,18) = HCF(172,77) = HCF(249,172) = HCF(421,249) = HCF(3617,421) .

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Frequently Asked Questions on HCF of 3617, 421 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 3617, 421?

Answer: HCF of 3617, 421 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 3617, 421 using Euclid's Algorithm?

Answer: For arbitrary numbers 3617, 421 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.