Highest Common Factor of 261, 501, 260 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, 501, 260 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 261, 501, 260 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, 501, 260 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, 501, 260 is 1.

HCF(261, 501, 260) = 1

HCF of 261, 501, 260 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, 501, 260 is 1.

Highest Common Factor of 261,501,260 using Euclid's algorithm

Highest Common Factor of 261,501,260 is 1

Step 1: Since 501 > 261, we apply the division lemma to 501 and 261, to get

501 = 261 x 1 + 240

Step 2: Since the reminder 261 ≠ 0, we apply division lemma to 240 and 261, to get

261 = 240 x 1 + 21

Step 3: We consider the new divisor 240 and the new remainder 21, and apply the division lemma to get

240 = 21 x 11 + 9

We consider the new divisor 21 and the new remainder 9,and apply the division lemma to get

21 = 9 x 2 + 3

We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get

9 = 3 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 261 and 501 is 3

Notice that 3 = HCF(9,3) = HCF(21,9) = HCF(240,21) = HCF(261,240) = HCF(501,261) .

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

Step 1: Since 260 > 3, we apply the division lemma to 260 and 3, to get

260 = 3 x 86 + 2

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get

3 = 2 x 1 + 1

Step 3: 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 3 and 260 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(260,3) .

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Frequently Asked Questions on HCF of 261, 501, 260 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, 501, 260?

Answer: HCF of 261, 501, 260 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 261, 501, 260 using Euclid's Algorithm?

Answer: For arbitrary numbers 261, 501, 260 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.