Highest Common Factor of 9101, 7554, 21852 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 9101, 7554, 21852 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 9101, 7554, 21852 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 9101, 7554, 21852 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 9101, 7554, 21852 is 1.

HCF(9101, 7554, 21852) = 1

HCF of 9101, 7554, 21852 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 9101, 7554, 21852 is 1.

Highest Common Factor of 9101,7554,21852 using Euclid's algorithm

Highest Common Factor of 9101,7554,21852 is 1

Step 1: Since 9101 > 7554, we apply the division lemma to 9101 and 7554, to get

9101 = 7554 x 1 + 1547

Step 2: Since the reminder 7554 ≠ 0, we apply division lemma to 1547 and 7554, to get

7554 = 1547 x 4 + 1366

Step 3: We consider the new divisor 1547 and the new remainder 1366, and apply the division lemma to get

1547 = 1366 x 1 + 181

We consider the new divisor 1366 and the new remainder 181,and apply the division lemma to get

1366 = 181 x 7 + 99

We consider the new divisor 181 and the new remainder 99,and apply the division lemma to get

181 = 99 x 1 + 82

We consider the new divisor 99 and the new remainder 82,and apply the division lemma to get

99 = 82 x 1 + 17

We consider the new divisor 82 and the new remainder 17,and apply the division lemma to get

82 = 17 x 4 + 14

We consider the new divisor 17 and the new remainder 14,and apply the division lemma to get

17 = 14 x 1 + 3

We consider the new divisor 14 and the new remainder 3,and apply the division lemma to get

14 = 3 x 4 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 9101 and 7554 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(14,3) = HCF(17,14) = HCF(82,17) = HCF(99,82) = HCF(181,99) = HCF(1366,181) = HCF(1547,1366) = HCF(7554,1547) = HCF(9101,7554) .

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

Step 1: Since 21852 > 1, we apply the division lemma to 21852 and 1, to get

21852 = 1 x 21852 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 21852 is 1

Notice that 1 = HCF(21852,1) .

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Frequently Asked Questions on HCF of 9101, 7554, 21852 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 9101, 7554, 21852?

Answer: HCF of 9101, 7554, 21852 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 9101, 7554, 21852 using Euclid's Algorithm?

Answer: For arbitrary numbers 9101, 7554, 21852 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.