Highest Common Factor of 409, 271, 523 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 409, 271, 523 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 409, 271, 523 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 409, 271, 523 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 409, 271, 523 is 1.

HCF(409, 271, 523) = 1

HCF of 409, 271, 523 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 409, 271, 523 is 1.

Highest Common Factor of 409,271,523 using Euclid's algorithm

Highest Common Factor of 409,271,523 is 1

Step 1: Since 409 > 271, we apply the division lemma to 409 and 271, to get

409 = 271 x 1 + 138

Step 2: Since the reminder 271 ≠ 0, we apply division lemma to 138 and 271, to get

271 = 138 x 1 + 133

Step 3: We consider the new divisor 138 and the new remainder 133, and apply the division lemma to get

138 = 133 x 1 + 5

We consider the new divisor 133 and the new remainder 5,and apply the division lemma to get

133 = 5 x 26 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 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 409 and 271 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(133,5) = HCF(138,133) = HCF(271,138) = HCF(409,271) .

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

Step 1: Since 523 > 1, we apply the division lemma to 523 and 1, to get

523 = 1 x 523 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 523 is 1

Notice that 1 = HCF(523,1) .

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Frequently Asked Questions on HCF of 409, 271, 523 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 409, 271, 523?

Answer: HCF of 409, 271, 523 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 409, 271, 523 using Euclid's Algorithm?

Answer: For arbitrary numbers 409, 271, 523 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.