Highest Common Factor of 3254, 8914, 14241 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 3254, 8914, 14241 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 3254, 8914, 14241 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 3254, 8914, 14241 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 3254, 8914, 14241 is 1.

HCF(3254, 8914, 14241) = 1

HCF of 3254, 8914, 14241 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 3254, 8914, 14241 is 1.

Highest Common Factor of 3254,8914,14241 using Euclid's algorithm

Highest Common Factor of 3254,8914,14241 is 1

Step 1: Since 8914 > 3254, we apply the division lemma to 8914 and 3254, to get

8914 = 3254 x 2 + 2406

Step 2: Since the reminder 3254 ≠ 0, we apply division lemma to 2406 and 3254, to get

3254 = 2406 x 1 + 848

Step 3: We consider the new divisor 2406 and the new remainder 848, and apply the division lemma to get

2406 = 848 x 2 + 710

We consider the new divisor 848 and the new remainder 710,and apply the division lemma to get

848 = 710 x 1 + 138

We consider the new divisor 710 and the new remainder 138,and apply the division lemma to get

710 = 138 x 5 + 20

We consider the new divisor 138 and the new remainder 20,and apply the division lemma to get

138 = 20 x 6 + 18

We consider the new divisor 20 and the new remainder 18,and apply the division lemma to get

20 = 18 x 1 + 2

We consider the new divisor 18 and the new remainder 2,and apply the division lemma to get

18 = 2 x 9 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 3254 and 8914 is 2

Notice that 2 = HCF(18,2) = HCF(20,18) = HCF(138,20) = HCF(710,138) = HCF(848,710) = HCF(2406,848) = HCF(3254,2406) = HCF(8914,3254) .

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

Step 1: Since 14241 > 2, we apply the division lemma to 14241 and 2, to get

14241 = 2 x 7120 + 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 14241 is 1

Notice that 1 = HCF(2,1) = HCF(14241,2) .

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Frequently Asked Questions on HCF of 3254, 8914, 14241 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 3254, 8914, 14241?

Answer: HCF of 3254, 8914, 14241 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 3254, 8914, 14241 using Euclid's Algorithm?

Answer: For arbitrary numbers 3254, 8914, 14241 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.