Highest Common Factor of 513, 731, 274 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 513, 731, 274 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 513, 731, 274 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 513, 731, 274 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 513, 731, 274 is 1.

HCF(513, 731, 274) = 1

HCF of 513, 731, 274 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 513, 731, 274 is 1.

Highest Common Factor of 513,731,274 using Euclid's algorithm

Highest Common Factor of 513,731,274 is 1

Step 1: Since 731 > 513, we apply the division lemma to 731 and 513, to get

731 = 513 x 1 + 218

Step 2: Since the reminder 513 ≠ 0, we apply division lemma to 218 and 513, to get

513 = 218 x 2 + 77

Step 3: We consider the new divisor 218 and the new remainder 77, and apply the division lemma to get

218 = 77 x 2 + 64

We consider the new divisor 77 and the new remainder 64,and apply the division lemma to get

77 = 64 x 1 + 13

We consider the new divisor 64 and the new remainder 13,and apply the division lemma to get

64 = 13 x 4 + 12

We consider the new divisor 13 and the new remainder 12,and apply the division lemma to get

13 = 12 x 1 + 1

We consider the new divisor 12 and the new remainder 1,and apply the division lemma to get

12 = 1 x 12 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 513 and 731 is 1

Notice that 1 = HCF(12,1) = HCF(13,12) = HCF(64,13) = HCF(77,64) = HCF(218,77) = HCF(513,218) = HCF(731,513) .

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

Step 1: Since 274 > 1, we apply the division lemma to 274 and 1, to get

274 = 1 x 274 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 274 is 1

Notice that 1 = HCF(274,1) .

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Frequently Asked Questions on HCF of 513, 731, 274 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 513, 731, 274?

Answer: HCF of 513, 731, 274 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 513, 731, 274 using Euclid's Algorithm?

Answer: For arbitrary numbers 513, 731, 274 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.