Highest Common Factor of 9614, 9851, 14963 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 9614, 9851, 14963 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 9614, 9851, 14963 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 9614, 9851, 14963 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 9614, 9851, 14963 is 1.

HCF(9614, 9851, 14963) = 1

HCF of 9614, 9851, 14963 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 9614, 9851, 14963 is 1.

Highest Common Factor of 9614,9851,14963 using Euclid's algorithm

Highest Common Factor of 9614,9851,14963 is 1

Step 1: Since 9851 > 9614, we apply the division lemma to 9851 and 9614, to get

9851 = 9614 x 1 + 237

Step 2: Since the reminder 9614 ≠ 0, we apply division lemma to 237 and 9614, to get

9614 = 237 x 40 + 134

Step 3: We consider the new divisor 237 and the new remainder 134, and apply the division lemma to get

237 = 134 x 1 + 103

We consider the new divisor 134 and the new remainder 103,and apply the division lemma to get

134 = 103 x 1 + 31

We consider the new divisor 103 and the new remainder 31,and apply the division lemma to get

103 = 31 x 3 + 10

We consider the new divisor 31 and the new remainder 10,and apply the division lemma to get

31 = 10 x 3 + 1

We consider the new divisor 10 and the new remainder 1,and apply the division lemma to get

10 = 1 x 10 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 9614 and 9851 is 1

Notice that 1 = HCF(10,1) = HCF(31,10) = HCF(103,31) = HCF(134,103) = HCF(237,134) = HCF(9614,237) = HCF(9851,9614) .

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

Step 1: Since 14963 > 1, we apply the division lemma to 14963 and 1, to get

14963 = 1 x 14963 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 14963 is 1

Notice that 1 = HCF(14963,1) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 9614, 9851, 14963 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 9614, 9851, 14963?

Answer: HCF of 9614, 9851, 14963 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 9614, 9851, 14963 using Euclid's Algorithm?

Answer: For arbitrary numbers 9614, 9851, 14963 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.