Highest Common Factor of 671, 420, 669 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, 420, 669 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 671, 420, 669 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, 420, 669 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, 420, 669 is 1.

HCF(671, 420, 669) = 1

HCF of 671, 420, 669 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, 420, 669 is 1.

Highest Common Factor of 671,420,669 using Euclid's algorithm

Highest Common Factor of 671,420,669 is 1

Step 1: Since 671 > 420, we apply the division lemma to 671 and 420, to get

671 = 420 x 1 + 251

Step 2: Since the reminder 420 ≠ 0, we apply division lemma to 251 and 420, to get

420 = 251 x 1 + 169

Step 3: We consider the new divisor 251 and the new remainder 169, and apply the division lemma to get

251 = 169 x 1 + 82

We consider the new divisor 169 and the new remainder 82,and apply the division lemma to get

169 = 82 x 2 + 5

We consider the new divisor 82 and the new remainder 5,and apply the division lemma to get

82 = 5 x 16 + 2

We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get

5 = 2 x 2 + 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 671 and 420 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(82,5) = HCF(169,82) = HCF(251,169) = HCF(420,251) = HCF(671,420) .

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

Step 1: Since 669 > 1, we apply the division lemma to 669 and 1, to get

669 = 1 x 669 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 669 is 1

Notice that 1 = HCF(669,1) .

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Frequently Asked Questions on HCF of 671, 420, 669 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, 420, 669?

Answer: HCF of 671, 420, 669 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 671, 420, 669 using Euclid's Algorithm?

Answer: For arbitrary numbers 671, 420, 669 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.