Highest Common Factor of 4113, 2974 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 4113, 2974 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 4113, 2974 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 4113, 2974 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 4113, 2974 is 1.

HCF(4113, 2974) = 1

HCF of 4113, 2974 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 4113, 2974 is 1.

Highest Common Factor of 4113,2974 using Euclid's algorithm

Highest Common Factor of 4113,2974 is 1

Step 1: Since 4113 > 2974, we apply the division lemma to 4113 and 2974, to get

4113 = 2974 x 1 + 1139

Step 2: Since the reminder 2974 ≠ 0, we apply division lemma to 1139 and 2974, to get

2974 = 1139 x 2 + 696

Step 3: We consider the new divisor 1139 and the new remainder 696, and apply the division lemma to get

1139 = 696 x 1 + 443

We consider the new divisor 696 and the new remainder 443,and apply the division lemma to get

696 = 443 x 1 + 253

We consider the new divisor 443 and the new remainder 253,and apply the division lemma to get

443 = 253 x 1 + 190

We consider the new divisor 253 and the new remainder 190,and apply the division lemma to get

253 = 190 x 1 + 63

We consider the new divisor 190 and the new remainder 63,and apply the division lemma to get

190 = 63 x 3 + 1

We consider the new divisor 63 and the new remainder 1,and apply the division lemma to get

63 = 1 x 63 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 4113 and 2974 is 1

Notice that 1 = HCF(63,1) = HCF(190,63) = HCF(253,190) = HCF(443,253) = HCF(696,443) = HCF(1139,696) = HCF(2974,1139) = HCF(4113,2974) .

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Frequently Asked Questions on HCF of 4113, 2974 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 4113, 2974?

Answer: HCF of 4113, 2974 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 4113, 2974 using Euclid's Algorithm?

Answer: For arbitrary numbers 4113, 2974 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.