Highest Common Factor of 417, 673 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, 673 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 417, 673 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, 673 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, 673 is 1.

HCF(417, 673) = 1

HCF of 417, 673 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, 673 is 1.

Highest Common Factor of 417,673 using Euclid's algorithm

Highest Common Factor of 417,673 is 1

Step 1: Since 673 > 417, we apply the division lemma to 673 and 417, to get

673 = 417 x 1 + 256

Step 2: Since the reminder 417 ≠ 0, we apply division lemma to 256 and 417, to get

417 = 256 x 1 + 161

Step 3: We consider the new divisor 256 and the new remainder 161, and apply the division lemma to get

256 = 161 x 1 + 95

We consider the new divisor 161 and the new remainder 95,and apply the division lemma to get

161 = 95 x 1 + 66

We consider the new divisor 95 and the new remainder 66,and apply the division lemma to get

95 = 66 x 1 + 29

We consider the new divisor 66 and the new remainder 29,and apply the division lemma to get

66 = 29 x 2 + 8

We consider the new divisor 29 and the new remainder 8,and apply the division lemma to get

29 = 8 x 3 + 5

We consider the new divisor 8 and the new remainder 5,and apply the division lemma to get

8 = 5 x 1 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 417 and 673 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(29,8) = HCF(66,29) = HCF(95,66) = HCF(161,95) = HCF(256,161) = HCF(417,256) = HCF(673,417) .

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Frequently Asked Questions on HCF of 417, 673 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, 673?

Answer: HCF of 417, 673 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 417, 673 using Euclid's Algorithm?

Answer: For arbitrary numbers 417, 673 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.