Highest Common Factor of 377, 614, 31 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 377, 614, 31 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 377, 614, 31 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 377, 614, 31 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 377, 614, 31 is 1.

HCF(377, 614, 31) = 1

HCF of 377, 614, 31 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 377, 614, 31 is 1.

Highest Common Factor of 377,614,31 using Euclid's algorithm

Highest Common Factor of 377,614,31 is 1

Step 1: Since 614 > 377, we apply the division lemma to 614 and 377, to get

614 = 377 x 1 + 237

Step 2: Since the reminder 377 ≠ 0, we apply division lemma to 237 and 377, to get

377 = 237 x 1 + 140

Step 3: We consider the new divisor 237 and the new remainder 140, and apply the division lemma to get

237 = 140 x 1 + 97

We consider the new divisor 140 and the new remainder 97,and apply the division lemma to get

140 = 97 x 1 + 43

We consider the new divisor 97 and the new remainder 43,and apply the division lemma to get

97 = 43 x 2 + 11

We consider the new divisor 43 and the new remainder 11,and apply the division lemma to get

43 = 11 x 3 + 10

We consider the new divisor 11 and the new remainder 10,and apply the division lemma to get

11 = 10 x 1 + 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 377 and 614 is 1

Notice that 1 = HCF(10,1) = HCF(11,10) = HCF(43,11) = HCF(97,43) = HCF(140,97) = HCF(237,140) = HCF(377,237) = HCF(614,377) .

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

Step 1: Since 31 > 1, we apply the division lemma to 31 and 1, to get

31 = 1 x 31 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 31 is 1

Notice that 1 = HCF(31,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 377, 614, 31 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 377, 614, 31?

Answer: HCF of 377, 614, 31 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 377, 614, 31 using Euclid's Algorithm?

Answer: For arbitrary numbers 377, 614, 31 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.