Highest Common Factor of 9213, 8521, 24177 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 9213, 8521, 24177 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 9213, 8521, 24177 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 9213, 8521, 24177 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 9213, 8521, 24177 is 1.

HCF(9213, 8521, 24177) = 1

HCF of 9213, 8521, 24177 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 9213, 8521, 24177 is 1.

Highest Common Factor of 9213,8521,24177 using Euclid's algorithm

Highest Common Factor of 9213,8521,24177 is 1

Step 1: Since 9213 > 8521, we apply the division lemma to 9213 and 8521, to get

9213 = 8521 x 1 + 692

Step 2: Since the reminder 8521 ≠ 0, we apply division lemma to 692 and 8521, to get

8521 = 692 x 12 + 217

Step 3: We consider the new divisor 692 and the new remainder 217, and apply the division lemma to get

692 = 217 x 3 + 41

We consider the new divisor 217 and the new remainder 41,and apply the division lemma to get

217 = 41 x 5 + 12

We consider the new divisor 41 and the new remainder 12,and apply the division lemma to get

41 = 12 x 3 + 5

We consider the new divisor 12 and the new remainder 5,and apply the division lemma to get

12 = 5 x 2 + 2

We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get

5 = 2 x 2 + 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 9213 and 8521 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(12,5) = HCF(41,12) = HCF(217,41) = HCF(692,217) = HCF(8521,692) = HCF(9213,8521) .

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

Step 1: Since 24177 > 1, we apply the division lemma to 24177 and 1, to get

24177 = 1 x 24177 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 24177 is 1

Notice that 1 = HCF(24177,1) .

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Frequently Asked Questions on HCF of 9213, 8521, 24177 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 9213, 8521, 24177?

Answer: HCF of 9213, 8521, 24177 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 9213, 8521, 24177 using Euclid's Algorithm?

Answer: For arbitrary numbers 9213, 8521, 24177 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.