Highest Common Factor of 4121, 7110 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 4121, 7110 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 4121, 7110 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 4121, 7110 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 4121, 7110 is 1.

HCF(4121, 7110) = 1

HCF of 4121, 7110 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

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Highest common factor (HCF) of 4121, 7110 is 1.

Highest Common Factor of 4121,7110 using Euclid's algorithm

Highest Common Factor of 4121,7110 is 1

Step 1: Since 7110 > 4121, we apply the division lemma to 7110 and 4121, to get

7110 = 4121 x 1 + 2989

Step 2: Since the reminder 4121 ≠ 0, we apply division lemma to 2989 and 4121, to get

4121 = 2989 x 1 + 1132

Step 3: We consider the new divisor 2989 and the new remainder 1132, and apply the division lemma to get

2989 = 1132 x 2 + 725

We consider the new divisor 1132 and the new remainder 725,and apply the division lemma to get

1132 = 725 x 1 + 407

We consider the new divisor 725 and the new remainder 407,and apply the division lemma to get

725 = 407 x 1 + 318

We consider the new divisor 407 and the new remainder 318,and apply the division lemma to get

407 = 318 x 1 + 89

We consider the new divisor 318 and the new remainder 89,and apply the division lemma to get

318 = 89 x 3 + 51

We consider the new divisor 89 and the new remainder 51,and apply the division lemma to get

89 = 51 x 1 + 38

We consider the new divisor 51 and the new remainder 38,and apply the division lemma to get

51 = 38 x 1 + 13

We consider the new divisor 38 and the new remainder 13,and apply the division lemma to get

38 = 13 x 2 + 12

We consider the new divisor 13 and the new remainder 12,and apply the division lemma to get

13 = 12 x 1 + 1

We consider the new divisor 12 and the new remainder 1,and apply the division lemma to get

12 = 1 x 12 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 4121 and 7110 is 1

Notice that 1 = HCF(12,1) = HCF(13,12) = HCF(38,13) = HCF(51,38) = HCF(89,51) = HCF(318,89) = HCF(407,318) = HCF(725,407) = HCF(1132,725) = HCF(2989,1132) = HCF(4121,2989) = HCF(7110,4121) .

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Frequently Asked Questions on HCF of 4121, 7110 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 4121, 7110?

Answer: HCF of 4121, 7110 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 4121, 7110 using Euclid's Algorithm?

Answer: For arbitrary numbers 4121, 7110 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.