Highest Common Factor of 221, 721, 614 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 221, 721, 614 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 221, 721, 614 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 221, 721, 614 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 221, 721, 614 is 1.

HCF(221, 721, 614) = 1

HCF of 221, 721, 614 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 221, 721, 614 is 1.

Highest Common Factor of 221,721,614 using Euclid's algorithm

Highest Common Factor of 221,721,614 is 1

Step 1: Since 721 > 221, we apply the division lemma to 721 and 221, to get

721 = 221 x 3 + 58

Step 2: Since the reminder 221 ≠ 0, we apply division lemma to 58 and 221, to get

221 = 58 x 3 + 47

Step 3: We consider the new divisor 58 and the new remainder 47, and apply the division lemma to get

58 = 47 x 1 + 11

We consider the new divisor 47 and the new remainder 11,and apply the division lemma to get

47 = 11 x 4 + 3

We consider the new divisor 11 and the new remainder 3,and apply the division lemma to get

11 = 3 x 3 + 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 221 and 721 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(11,3) = HCF(47,11) = HCF(58,47) = HCF(221,58) = HCF(721,221) .

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

Step 1: Since 614 > 1, we apply the division lemma to 614 and 1, to get

614 = 1 x 614 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 614 is 1

Notice that 1 = HCF(614,1) .

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Frequently Asked Questions on HCF of 221, 721, 614 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 221, 721, 614?

Answer: HCF of 221, 721, 614 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 221, 721, 614 using Euclid's Algorithm?

Answer: For arbitrary numbers 221, 721, 614 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.