Highest Common Factor of 538, 729, 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 538, 729, 260 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 538, 729, 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 538, 729, 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 538, 729, 260 is 1.

HCF(538, 729, 260) = 1

HCF of 538, 729, 260 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 538, 729, 260 is 1.

Highest Common Factor of 538,729,260 using Euclid's algorithm

Highest Common Factor of 538,729,260 is 1

Step 1: Since 729 > 538, we apply the division lemma to 729 and 538, to get

729 = 538 x 1 + 191

Step 2: Since the reminder 538 ≠ 0, we apply division lemma to 191 and 538, to get

538 = 191 x 2 + 156

Step 3: We consider the new divisor 191 and the new remainder 156, and apply the division lemma to get

191 = 156 x 1 + 35

We consider the new divisor 156 and the new remainder 35,and apply the division lemma to get

156 = 35 x 4 + 16

We consider the new divisor 35 and the new remainder 16,and apply the division lemma to get

35 = 16 x 2 + 3

We consider the new divisor 16 and the new remainder 3,and apply the division lemma to get

16 = 3 x 5 + 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 538 and 729 is 1

Notice that 1 = HCF(3,1) = HCF(16,3) = HCF(35,16) = HCF(156,35) = HCF(191,156) = HCF(538,191) = HCF(729,538) .

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

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

260 = 1 x 260 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 260 is 1

Notice that 1 = HCF(260,1) .

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Frequently Asked Questions on HCF of 538, 729, 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 538, 729, 260?

Answer: HCF of 538, 729, 260 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 538, 729, 260 using Euclid's Algorithm?

Answer: For arbitrary numbers 538, 729, 260 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.