Highest Common Factor of 677, 390, 583 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, 390, 583 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 677, 390, 583 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, 390, 583 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, 390, 583 is 1.

HCF(677, 390, 583) = 1

HCF of 677, 390, 583 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, 390, 583 is 1.

Highest Common Factor of 677,390,583 using Euclid's algorithm

Highest Common Factor of 677,390,583 is 1

Step 1: Since 677 > 390, we apply the division lemma to 677 and 390, to get

677 = 390 x 1 + 287

Step 2: Since the reminder 390 ≠ 0, we apply division lemma to 287 and 390, to get

390 = 287 x 1 + 103

Step 3: We consider the new divisor 287 and the new remainder 103, and apply the division lemma to get

287 = 103 x 2 + 81

We consider the new divisor 103 and the new remainder 81,and apply the division lemma to get

103 = 81 x 1 + 22

We consider the new divisor 81 and the new remainder 22,and apply the division lemma to get

81 = 22 x 3 + 15

We consider the new divisor 22 and the new remainder 15,and apply the division lemma to get

22 = 15 x 1 + 7

We consider the new divisor 15 and the new remainder 7,and apply the division lemma to get

15 = 7 x 2 + 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 677 and 390 is 1

Notice that 1 = HCF(7,1) = HCF(15,7) = HCF(22,15) = HCF(81,22) = HCF(103,81) = HCF(287,103) = HCF(390,287) = HCF(677,390) .

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

Step 1: Since 583 > 1, we apply the division lemma to 583 and 1, to get

583 = 1 x 583 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 583 is 1

Notice that 1 = HCF(583,1) .

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Frequently Asked Questions on HCF of 677, 390, 583 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, 390, 583?

Answer: HCF of 677, 390, 583 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 677, 390, 583 using Euclid's Algorithm?

Answer: For arbitrary numbers 677, 390, 583 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.