Highest Common Factor of 9917, 1114 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 9917, 1114 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 9917, 1114 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 9917, 1114 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 9917, 1114 is 1.

HCF(9917, 1114) = 1

HCF of 9917, 1114 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 9917, 1114 is 1.

Highest Common Factor of 9917,1114 using Euclid's algorithm

Highest Common Factor of 9917,1114 is 1

Step 1: Since 9917 > 1114, we apply the division lemma to 9917 and 1114, to get

9917 = 1114 x 8 + 1005

Step 2: Since the reminder 1114 ≠ 0, we apply division lemma to 1005 and 1114, to get

1114 = 1005 x 1 + 109

Step 3: We consider the new divisor 1005 and the new remainder 109, and apply the division lemma to get

1005 = 109 x 9 + 24

We consider the new divisor 109 and the new remainder 24,and apply the division lemma to get

109 = 24 x 4 + 13

We consider the new divisor 24 and the new remainder 13,and apply the division lemma to get

24 = 13 x 1 + 11

We consider the new divisor 13 and the new remainder 11,and apply the division lemma to get

13 = 11 x 1 + 2

We consider the new divisor 11 and the new remainder 2,and apply the division lemma to get

11 = 2 x 5 + 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 9917 and 1114 is 1

Notice that 1 = HCF(2,1) = HCF(11,2) = HCF(13,11) = HCF(24,13) = HCF(109,24) = HCF(1005,109) = HCF(1114,1005) = HCF(9917,1114) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 9917, 1114 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 9917, 1114?

Answer: HCF of 9917, 1114 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 9917, 1114 using Euclid's Algorithm?

Answer: For arbitrary numbers 9917, 1114 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.