Highest Common Factor of 853, 9149, 9377 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 853, 9149, 9377 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 853, 9149, 9377 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 853, 9149, 9377 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 853, 9149, 9377 is 1.

HCF(853, 9149, 9377) = 1

HCF of 853, 9149, 9377 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 853, 9149, 9377 is 1.

Highest Common Factor of 853,9149,9377 using Euclid's algorithm

Highest Common Factor of 853,9149,9377 is 1

Step 1: Since 9149 > 853, we apply the division lemma to 9149 and 853, to get

9149 = 853 x 10 + 619

Step 2: Since the reminder 853 ≠ 0, we apply division lemma to 619 and 853, to get

853 = 619 x 1 + 234

Step 3: We consider the new divisor 619 and the new remainder 234, and apply the division lemma to get

619 = 234 x 2 + 151

We consider the new divisor 234 and the new remainder 151,and apply the division lemma to get

234 = 151 x 1 + 83

We consider the new divisor 151 and the new remainder 83,and apply the division lemma to get

151 = 83 x 1 + 68

We consider the new divisor 83 and the new remainder 68,and apply the division lemma to get

83 = 68 x 1 + 15

We consider the new divisor 68 and the new remainder 15,and apply the division lemma to get

68 = 15 x 4 + 8

We consider the new divisor 15 and the new remainder 8,and apply the division lemma to get

15 = 8 x 1 + 7

We consider the new divisor 8 and the new remainder 7,and apply the division lemma to get

8 = 7 x 1 + 1

We consider the new divisor 7 and the new remainder 1,and apply the division lemma to get

7 = 1 x 7 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 853 and 9149 is 1

Notice that 1 = HCF(7,1) = HCF(8,7) = HCF(15,8) = HCF(68,15) = HCF(83,68) = HCF(151,83) = HCF(234,151) = HCF(619,234) = HCF(853,619) = HCF(9149,853) .

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

Step 1: Since 9377 > 1, we apply the division lemma to 9377 and 1, to get

9377 = 1 x 9377 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 9377 is 1

Notice that 1 = HCF(9377,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 853, 9149, 9377 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 853, 9149, 9377?

Answer: HCF of 853, 9149, 9377 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 853, 9149, 9377 using Euclid's Algorithm?

Answer: For arbitrary numbers 853, 9149, 9377 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.