Highest Common Factor of 9138, 9214, 24625 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 9138, 9214, 24625 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 9138, 9214, 24625 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 9138, 9214, 24625 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 9138, 9214, 24625 is 1.

HCF(9138, 9214, 24625) = 1

HCF of 9138, 9214, 24625 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 9138, 9214, 24625 is 1.

Highest Common Factor of 9138,9214,24625 using Euclid's algorithm

Highest Common Factor of 9138,9214,24625 is 1

Step 1: Since 9214 > 9138, we apply the division lemma to 9214 and 9138, to get

9214 = 9138 x 1 + 76

Step 2: Since the reminder 9138 ≠ 0, we apply division lemma to 76 and 9138, to get

9138 = 76 x 120 + 18

Step 3: We consider the new divisor 76 and the new remainder 18, and apply the division lemma to get

76 = 18 x 4 + 4

We consider the new divisor 18 and the new remainder 4,and apply the division lemma to get

18 = 4 x 4 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 9138 and 9214 is 2

Notice that 2 = HCF(4,2) = HCF(18,4) = HCF(76,18) = HCF(9138,76) = HCF(9214,9138) .

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

Step 1: Since 24625 > 2, we apply the division lemma to 24625 and 2, to get

24625 = 2 x 12312 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 24625 is 1

Notice that 1 = HCF(2,1) = HCF(24625,2) .

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Frequently Asked Questions on HCF of 9138, 9214, 24625 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 9138, 9214, 24625?

Answer: HCF of 9138, 9214, 24625 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 9138, 9214, 24625 using Euclid's Algorithm?

Answer: For arbitrary numbers 9138, 9214, 24625 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.