Highest Common Factor of 677, 780, 249 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 677, 780, 249 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 677, 780, 249 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 677, 780, 249 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 677, 780, 249 is 1.

HCF(677, 780, 249) = 1

HCF of 677, 780, 249 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 677, 780, 249 is 1.

Highest Common Factor of 677,780,249 using Euclid's algorithm

Highest Common Factor of 677,780,249 is 1

Step 1: Since 780 > 677, we apply the division lemma to 780 and 677, to get

780 = 677 x 1 + 103

Step 2: Since the reminder 677 ≠ 0, we apply division lemma to 103 and 677, to get

677 = 103 x 6 + 59

Step 3: We consider the new divisor 103 and the new remainder 59, and apply the division lemma to get

103 = 59 x 1 + 44

We consider the new divisor 59 and the new remainder 44,and apply the division lemma to get

59 = 44 x 1 + 15

We consider the new divisor 44 and the new remainder 15,and apply the division lemma to get

44 = 15 x 2 + 14

We consider the new divisor 15 and the new remainder 14,and apply the division lemma to get

15 = 14 x 1 + 1

We consider the new divisor 14 and the new remainder 1,and apply the division lemma to get

14 = 1 x 14 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 677 and 780 is 1

Notice that 1 = HCF(14,1) = HCF(15,14) = HCF(44,15) = HCF(59,44) = HCF(103,59) = HCF(677,103) = HCF(780,677) .

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

Step 1: Since 249 > 1, we apply the division lemma to 249 and 1, to get

249 = 1 x 249 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 249 is 1

Notice that 1 = HCF(249,1) .

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Frequently Asked Questions on HCF of 677, 780, 249 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 677, 780, 249?

Answer: HCF of 677, 780, 249 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 677, 780, 249 using Euclid's Algorithm?

Answer: For arbitrary numbers 677, 780, 249 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.