Highest Common Factor of 3457, 2108 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 3457, 2108 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 3457, 2108 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 3457, 2108 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 3457, 2108 is 1.

HCF(3457, 2108) = 1

HCF of 3457, 2108 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 3457, 2108 is 1.

Highest Common Factor of 3457,2108 using Euclid's algorithm

Highest Common Factor of 3457,2108 is 1

Step 1: Since 3457 > 2108, we apply the division lemma to 3457 and 2108, to get

3457 = 2108 x 1 + 1349

Step 2: Since the reminder 2108 ≠ 0, we apply division lemma to 1349 and 2108, to get

2108 = 1349 x 1 + 759

Step 3: We consider the new divisor 1349 and the new remainder 759, and apply the division lemma to get

1349 = 759 x 1 + 590

We consider the new divisor 759 and the new remainder 590,and apply the division lemma to get

759 = 590 x 1 + 169

We consider the new divisor 590 and the new remainder 169,and apply the division lemma to get

590 = 169 x 3 + 83

We consider the new divisor 169 and the new remainder 83,and apply the division lemma to get

169 = 83 x 2 + 3

We consider the new divisor 83 and the new remainder 3,and apply the division lemma to get

83 = 3 x 27 + 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 3457 and 2108 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(83,3) = HCF(169,83) = HCF(590,169) = HCF(759,590) = HCF(1349,759) = HCF(2108,1349) = HCF(3457,2108) .

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Frequently Asked Questions on HCF of 3457, 2108 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 3457, 2108?

Answer: HCF of 3457, 2108 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 3457, 2108 using Euclid's Algorithm?

Answer: For arbitrary numbers 3457, 2108 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.