Highest Common Factor of 8502, 9915, 23185 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 8502, 9915, 23185 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 8502, 9915, 23185 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 8502, 9915, 23185 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 8502, 9915, 23185 is 1.

HCF(8502, 9915, 23185) = 1

HCF of 8502, 9915, 23185 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 8502, 9915, 23185 is 1.

Highest Common Factor of 8502,9915,23185 using Euclid's algorithm

Highest Common Factor of 8502,9915,23185 is 1

Step 1: Since 9915 > 8502, we apply the division lemma to 9915 and 8502, to get

9915 = 8502 x 1 + 1413

Step 2: Since the reminder 8502 ≠ 0, we apply division lemma to 1413 and 8502, to get

8502 = 1413 x 6 + 24

Step 3: We consider the new divisor 1413 and the new remainder 24, and apply the division lemma to get

1413 = 24 x 58 + 21

We consider the new divisor 24 and the new remainder 21,and apply the division lemma to get

24 = 21 x 1 + 3

We consider the new divisor 21 and the new remainder 3,and apply the division lemma to get

21 = 3 x 7 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 8502 and 9915 is 3

Notice that 3 = HCF(21,3) = HCF(24,21) = HCF(1413,24) = HCF(8502,1413) = HCF(9915,8502) .

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

Step 1: Since 23185 > 3, we apply the division lemma to 23185 and 3, to get

23185 = 3 x 7728 + 1

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 23185 is 1

Notice that 1 = HCF(3,1) = HCF(23185,3) .

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Frequently Asked Questions on HCF of 8502, 9915, 23185 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 8502, 9915, 23185?

Answer: HCF of 8502, 9915, 23185 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 8502, 9915, 23185 using Euclid's Algorithm?

Answer: For arbitrary numbers 8502, 9915, 23185 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.