Highest Common Factor of 9586, 7516 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 9586, 7516 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 9586, 7516 is 2 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 9586, 7516 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 9586, 7516 is 2.

HCF(9586, 7516) = 2

HCF of 9586, 7516 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 9586, 7516 is 2.

Highest Common Factor of 9586,7516 using Euclid's algorithm

Highest Common Factor of 9586,7516 is 2

Step 1: Since 9586 > 7516, we apply the division lemma to 9586 and 7516, to get

9586 = 7516 x 1 + 2070

Step 2: Since the reminder 7516 ≠ 0, we apply division lemma to 2070 and 7516, to get

7516 = 2070 x 3 + 1306

Step 3: We consider the new divisor 2070 and the new remainder 1306, and apply the division lemma to get

2070 = 1306 x 1 + 764

We consider the new divisor 1306 and the new remainder 764,and apply the division lemma to get

1306 = 764 x 1 + 542

We consider the new divisor 764 and the new remainder 542,and apply the division lemma to get

764 = 542 x 1 + 222

We consider the new divisor 542 and the new remainder 222,and apply the division lemma to get

542 = 222 x 2 + 98

We consider the new divisor 222 and the new remainder 98,and apply the division lemma to get

222 = 98 x 2 + 26

We consider the new divisor 98 and the new remainder 26,and apply the division lemma to get

98 = 26 x 3 + 20

We consider the new divisor 26 and the new remainder 20,and apply the division lemma to get

26 = 20 x 1 + 6

We consider the new divisor 20 and the new remainder 6,and apply the division lemma to get

20 = 6 x 3 + 2

We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get

6 = 2 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 9586 and 7516 is 2

Notice that 2 = HCF(6,2) = HCF(20,6) = HCF(26,20) = HCF(98,26) = HCF(222,98) = HCF(542,222) = HCF(764,542) = HCF(1306,764) = HCF(2070,1306) = HCF(7516,2070) = HCF(9586,7516) .

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Frequently Asked Questions on HCF of 9586, 7516 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 9586, 7516?

Answer: HCF of 9586, 7516 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 9586, 7516 using Euclid's Algorithm?

Answer: For arbitrary numbers 9586, 7516 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.