Highest Common Factor of 221, 7454, 6210 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, 7454, 6210 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 221, 7454, 6210 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, 7454, 6210 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, 7454, 6210 is 1.

HCF(221, 7454, 6210) = 1

HCF of 221, 7454, 6210 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, 7454, 6210 is 1.

Highest Common Factor of 221,7454,6210 using Euclid's algorithm

Highest Common Factor of 221,7454,6210 is 1

Step 1: Since 7454 > 221, we apply the division lemma to 7454 and 221, to get

7454 = 221 x 33 + 161

Step 2: Since the reminder 221 ≠ 0, we apply division lemma to 161 and 221, to get

221 = 161 x 1 + 60

Step 3: We consider the new divisor 161 and the new remainder 60, and apply the division lemma to get

161 = 60 x 2 + 41

We consider the new divisor 60 and the new remainder 41,and apply the division lemma to get

60 = 41 x 1 + 19

We consider the new divisor 41 and the new remainder 19,and apply the division lemma to get

41 = 19 x 2 + 3

We consider the new divisor 19 and the new remainder 3,and apply the division lemma to get

19 = 3 x 6 + 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 221 and 7454 is 1

Notice that 1 = HCF(3,1) = HCF(19,3) = HCF(41,19) = HCF(60,41) = HCF(161,60) = HCF(221,161) = HCF(7454,221) .

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

Step 1: Since 6210 > 1, we apply the division lemma to 6210 and 1, to get

6210 = 1 x 6210 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 6210 is 1

Notice that 1 = HCF(6210,1) .

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Frequently Asked Questions on HCF of 221, 7454, 6210 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, 7454, 6210?

Answer: HCF of 221, 7454, 6210 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 221, 7454, 6210 using Euclid's Algorithm?

Answer: For arbitrary numbers 221, 7454, 6210 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.