Highest Common Factor of 854, 677, 137 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 854, 677, 137 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 854, 677, 137 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 854, 677, 137 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 854, 677, 137 is 1.

HCF(854, 677, 137) = 1

HCF of 854, 677, 137 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 854, 677, 137 is 1.

Highest Common Factor of 854,677,137 using Euclid's algorithm

Highest Common Factor of 854,677,137 is 1

Step 1: Since 854 > 677, we apply the division lemma to 854 and 677, to get

854 = 677 x 1 + 177

Step 2: Since the reminder 677 ≠ 0, we apply division lemma to 177 and 677, to get

677 = 177 x 3 + 146

Step 3: We consider the new divisor 177 and the new remainder 146, and apply the division lemma to get

177 = 146 x 1 + 31

We consider the new divisor 146 and the new remainder 31,and apply the division lemma to get

146 = 31 x 4 + 22

We consider the new divisor 31 and the new remainder 22,and apply the division lemma to get

31 = 22 x 1 + 9

We consider the new divisor 22 and the new remainder 9,and apply the division lemma to get

22 = 9 x 2 + 4

We consider the new divisor 9 and the new remainder 4,and apply the division lemma to get

9 = 4 x 2 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 854 and 677 is 1

Notice that 1 = HCF(4,1) = HCF(9,4) = HCF(22,9) = HCF(31,22) = HCF(146,31) = HCF(177,146) = HCF(677,177) = HCF(854,677) .

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

Step 1: Since 137 > 1, we apply the division lemma to 137 and 1, to get

137 = 1 x 137 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 137 is 1

Notice that 1 = HCF(137,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 854, 677, 137 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 854, 677, 137?

Answer: HCF of 854, 677, 137 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 854, 677, 137 using Euclid's Algorithm?

Answer: For arbitrary numbers 854, 677, 137 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.