Highest Common Factor of 261, 413 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 261, 413 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 261, 413 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 261, 413 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 261, 413 is 1.

HCF(261, 413) = 1

HCF of 261, 413 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

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Highest common factor (HCF) of 261, 413 is 1.

Highest Common Factor of 261,413 using Euclid's algorithm

Highest Common Factor of 261,413 is 1

Step 1: Since 413 > 261, we apply the division lemma to 413 and 261, to get

413 = 261 x 1 + 152

Step 2: Since the reminder 261 ≠ 0, we apply division lemma to 152 and 261, to get

261 = 152 x 1 + 109

Step 3: We consider the new divisor 152 and the new remainder 109, and apply the division lemma to get

152 = 109 x 1 + 43

We consider the new divisor 109 and the new remainder 43,and apply the division lemma to get

109 = 43 x 2 + 23

We consider the new divisor 43 and the new remainder 23,and apply the division lemma to get

43 = 23 x 1 + 20

We consider the new divisor 23 and the new remainder 20,and apply the division lemma to get

23 = 20 x 1 + 3

We consider the new divisor 20 and the new remainder 3,and apply the division lemma to get

20 = 3 x 6 + 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 261 and 413 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(20,3) = HCF(23,20) = HCF(43,23) = HCF(109,43) = HCF(152,109) = HCF(261,152) = HCF(413,261) .

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Frequently Asked Questions on HCF of 261, 413 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 261, 413?

Answer: HCF of 261, 413 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 261, 413 using Euclid's Algorithm?

Answer: For arbitrary numbers 261, 413 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.