Highest Common Factor of 7130, 6053 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 7130, 6053 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 7130, 6053 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 7130, 6053 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 7130, 6053 is 1.

HCF(7130, 6053) = 1

HCF of 7130, 6053 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 7130, 6053 is 1.

Highest Common Factor of 7130,6053 using Euclid's algorithm

Highest Common Factor of 7130,6053 is 1

Step 1: Since 7130 > 6053, we apply the division lemma to 7130 and 6053, to get

7130 = 6053 x 1 + 1077

Step 2: Since the reminder 6053 ≠ 0, we apply division lemma to 1077 and 6053, to get

6053 = 1077 x 5 + 668

Step 3: We consider the new divisor 1077 and the new remainder 668, and apply the division lemma to get

1077 = 668 x 1 + 409

We consider the new divisor 668 and the new remainder 409,and apply the division lemma to get

668 = 409 x 1 + 259

We consider the new divisor 409 and the new remainder 259,and apply the division lemma to get

409 = 259 x 1 + 150

We consider the new divisor 259 and the new remainder 150,and apply the division lemma to get

259 = 150 x 1 + 109

We consider the new divisor 150 and the new remainder 109,and apply the division lemma to get

150 = 109 x 1 + 41

We consider the new divisor 109 and the new remainder 41,and apply the division lemma to get

109 = 41 x 2 + 27

We consider the new divisor 41 and the new remainder 27,and apply the division lemma to get

41 = 27 x 1 + 14

We consider the new divisor 27 and the new remainder 14,and apply the division lemma to get

27 = 14 x 1 + 13

We consider the new divisor 14 and the new remainder 13,and apply the division lemma to get

14 = 13 x 1 + 1

We consider the new divisor 13 and the new remainder 1,and apply the division lemma to get

13 = 1 x 13 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 7130 and 6053 is 1

Notice that 1 = HCF(13,1) = HCF(14,13) = HCF(27,14) = HCF(41,27) = HCF(109,41) = HCF(150,109) = HCF(259,150) = HCF(409,259) = HCF(668,409) = HCF(1077,668) = HCF(6053,1077) = HCF(7130,6053) .

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Frequently Asked Questions on HCF of 7130, 6053 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 7130, 6053?

Answer: HCF of 7130, 6053 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 7130, 6053 using Euclid's Algorithm?

Answer: For arbitrary numbers 7130, 6053 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.