Highest Common Factor of 671, 417, 565 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 671, 417, 565 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 671, 417, 565 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 671, 417, 565 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 671, 417, 565 is 1.

HCF(671, 417, 565) = 1

HCF of 671, 417, 565 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 671, 417, 565 is 1.

Highest Common Factor of 671,417,565 using Euclid's algorithm

Highest Common Factor of 671,417,565 is 1

Step 1: Since 671 > 417, we apply the division lemma to 671 and 417, to get

671 = 417 x 1 + 254

Step 2: Since the reminder 417 ≠ 0, we apply division lemma to 254 and 417, to get

417 = 254 x 1 + 163

Step 3: We consider the new divisor 254 and the new remainder 163, and apply the division lemma to get

254 = 163 x 1 + 91

We consider the new divisor 163 and the new remainder 91,and apply the division lemma to get

163 = 91 x 1 + 72

We consider the new divisor 91 and the new remainder 72,and apply the division lemma to get

91 = 72 x 1 + 19

We consider the new divisor 72 and the new remainder 19,and apply the division lemma to get

72 = 19 x 3 + 15

We consider the new divisor 19 and the new remainder 15,and apply the division lemma to get

19 = 15 x 1 + 4

We consider the new divisor 15 and the new remainder 4,and apply the division lemma to get

15 = 4 x 3 + 3

We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get

4 = 3 x 1 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 671 and 417 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(15,4) = HCF(19,15) = HCF(72,19) = HCF(91,72) = HCF(163,91) = HCF(254,163) = HCF(417,254) = HCF(671,417) .

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

Step 1: Since 565 > 1, we apply the division lemma to 565 and 1, to get

565 = 1 x 565 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 565 is 1

Notice that 1 = HCF(565,1) .

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Frequently Asked Questions on HCF of 671, 417, 565 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 671, 417, 565?

Answer: HCF of 671, 417, 565 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 671, 417, 565 using Euclid's Algorithm?

Answer: For arbitrary numbers 671, 417, 565 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.