Highest Common Factor of 721, 462, 341 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 721, 462, 341 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 721, 462, 341 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 721, 462, 341 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 721, 462, 341 is 1.

HCF(721, 462, 341) = 1

HCF of 721, 462, 341 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 721, 462, 341 is 1.

Highest Common Factor of 721,462,341 using Euclid's algorithm

Highest Common Factor of 721,462,341 is 1

Step 1: Since 721 > 462, we apply the division lemma to 721 and 462, to get

721 = 462 x 1 + 259

Step 2: Since the reminder 462 ≠ 0, we apply division lemma to 259 and 462, to get

462 = 259 x 1 + 203

Step 3: We consider the new divisor 259 and the new remainder 203, and apply the division lemma to get

259 = 203 x 1 + 56

We consider the new divisor 203 and the new remainder 56,and apply the division lemma to get

203 = 56 x 3 + 35

We consider the new divisor 56 and the new remainder 35,and apply the division lemma to get

56 = 35 x 1 + 21

We consider the new divisor 35 and the new remainder 21,and apply the division lemma to get

35 = 21 x 1 + 14

We consider the new divisor 21 and the new remainder 14,and apply the division lemma to get

21 = 14 x 1 + 7

We consider the new divisor 14 and the new remainder 7,and apply the division lemma to get

14 = 7 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 721 and 462 is 7

Notice that 7 = HCF(14,7) = HCF(21,14) = HCF(35,21) = HCF(56,35) = HCF(203,56) = HCF(259,203) = HCF(462,259) = HCF(721,462) .

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

Step 1: Since 341 > 7, we apply the division lemma to 341 and 7, to get

341 = 7 x 48 + 5

Step 2: Since the reminder 7 ≠ 0, we apply division lemma to 5 and 7, to get

7 = 5 x 1 + 2

Step 3: 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 7 and 341 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(341,7) .

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Frequently Asked Questions on HCF of 721, 462, 341 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 721, 462, 341?

Answer: HCF of 721, 462, 341 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 721, 462, 341 using Euclid's Algorithm?

Answer: For arbitrary numbers 721, 462, 341 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.