Highest Common Factor of 9523, 9988, 27516 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 9523, 9988, 27516 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 9523, 9988, 27516 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 9523, 9988, 27516 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 9523, 9988, 27516 is 1.

HCF(9523, 9988, 27516) = 1

HCF of 9523, 9988, 27516 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 9523, 9988, 27516 is 1.

Highest Common Factor of 9523,9988,27516 using Euclid's algorithm

Highest Common Factor of 9523,9988,27516 is 1

Step 1: Since 9988 > 9523, we apply the division lemma to 9988 and 9523, to get

9988 = 9523 x 1 + 465

Step 2: Since the reminder 9523 ≠ 0, we apply division lemma to 465 and 9523, to get

9523 = 465 x 20 + 223

Step 3: We consider the new divisor 465 and the new remainder 223, and apply the division lemma to get

465 = 223 x 2 + 19

We consider the new divisor 223 and the new remainder 19,and apply the division lemma to get

223 = 19 x 11 + 14

We consider the new divisor 19 and the new remainder 14,and apply the division lemma to get

19 = 14 x 1 + 5

We consider the new divisor 14 and the new remainder 5,and apply the division lemma to get

14 = 5 x 2 + 4

We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get

5 = 4 x 1 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 9523 and 9988 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(14,5) = HCF(19,14) = HCF(223,19) = HCF(465,223) = HCF(9523,465) = HCF(9988,9523) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Step 1: Since 27516 > 1, we apply the division lemma to 27516 and 1, to get

27516 = 1 x 27516 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 27516 is 1

Notice that 1 = HCF(27516,1) .

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Frequently Asked Questions on HCF of 9523, 9988, 27516 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 9523, 9988, 27516?

Answer: HCF of 9523, 9988, 27516 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 9523, 9988, 27516 using Euclid's Algorithm?

Answer: For arbitrary numbers 9523, 9988, 27516 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.