Highest Common Factor of 331, 721, 173 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 331, 721, 173 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 331, 721, 173 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 331, 721, 173 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 331, 721, 173 is 1.

HCF(331, 721, 173) = 1

HCF of 331, 721, 173 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 331, 721, 173 is 1.

Highest Common Factor of 331,721,173 using Euclid's algorithm

Highest Common Factor of 331,721,173 is 1

Step 1: Since 721 > 331, we apply the division lemma to 721 and 331, to get

721 = 331 x 2 + 59

Step 2: Since the reminder 331 ≠ 0, we apply division lemma to 59 and 331, to get

331 = 59 x 5 + 36

Step 3: We consider the new divisor 59 and the new remainder 36, and apply the division lemma to get

59 = 36 x 1 + 23

We consider the new divisor 36 and the new remainder 23,and apply the division lemma to get

36 = 23 x 1 + 13

We consider the new divisor 23 and the new remainder 13,and apply the division lemma to get

23 = 13 x 1 + 10

We consider the new divisor 13 and the new remainder 10,and apply the division lemma to get

13 = 10 x 1 + 3

We consider the new divisor 10 and the new remainder 3,and apply the division lemma to get

10 = 3 x 3 + 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 331 and 721 is 1

Notice that 1 = HCF(3,1) = HCF(10,3) = HCF(13,10) = HCF(23,13) = HCF(36,23) = HCF(59,36) = HCF(331,59) = HCF(721,331) .

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

Step 1: Since 173 > 1, we apply the division lemma to 173 and 1, to get

173 = 1 x 173 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 173 is 1

Notice that 1 = HCF(173,1) .

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Frequently Asked Questions on HCF of 331, 721, 173 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 331, 721, 173?

Answer: HCF of 331, 721, 173 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 331, 721, 173 using Euclid's Algorithm?

Answer: For arbitrary numbers 331, 721, 173 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.