Highest Common Factor of 417, 677 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 417, 677 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 417, 677 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 417, 677 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 417, 677 is 1.

HCF(417, 677) = 1

HCF of 417, 677 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 417, 677 is 1.

Highest Common Factor of 417,677 using Euclid's algorithm

Highest Common Factor of 417,677 is 1

Step 1: Since 677 > 417, we apply the division lemma to 677 and 417, to get

677 = 417 x 1 + 260

Step 2: Since the reminder 417 ≠ 0, we apply division lemma to 260 and 417, to get

417 = 260 x 1 + 157

Step 3: We consider the new divisor 260 and the new remainder 157, and apply the division lemma to get

260 = 157 x 1 + 103

We consider the new divisor 157 and the new remainder 103,and apply the division lemma to get

157 = 103 x 1 + 54

We consider the new divisor 103 and the new remainder 54,and apply the division lemma to get

103 = 54 x 1 + 49

We consider the new divisor 54 and the new remainder 49,and apply the division lemma to get

54 = 49 x 1 + 5

We consider the new divisor 49 and the new remainder 5,and apply the division lemma to get

49 = 5 x 9 + 4

We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get

5 = 4 x 1 + 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 417 and 677 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(49,5) = HCF(54,49) = HCF(103,54) = HCF(157,103) = HCF(260,157) = HCF(417,260) = HCF(677,417) .

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Frequently Asked Questions on HCF of 417, 677 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 417, 677?

Answer: HCF of 417, 677 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 417, 677 using Euclid's Algorithm?

Answer: For arbitrary numbers 417, 677 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.