Highest Common Factor of 113, 516, 514 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 113, 516, 514 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 113, 516, 514 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 113, 516, 514 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 113, 516, 514 is 1.

HCF(113, 516, 514) = 1

HCF of 113, 516, 514 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 113, 516, 514 is 1.

Highest Common Factor of 113,516,514 using Euclid's algorithm

Highest Common Factor of 113,516,514 is 1

Step 1: Since 516 > 113, we apply the division lemma to 516 and 113, to get

516 = 113 x 4 + 64

Step 2: Since the reminder 113 ≠ 0, we apply division lemma to 64 and 113, to get

113 = 64 x 1 + 49

Step 3: We consider the new divisor 64 and the new remainder 49, and apply the division lemma to get

64 = 49 x 1 + 15

We consider the new divisor 49 and the new remainder 15,and apply the division lemma to get

49 = 15 x 3 + 4

We consider the new divisor 15 and the new remainder 4,and apply the division lemma to get

15 = 4 x 3 + 3

We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get

4 = 3 x 1 + 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 113 and 516 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(15,4) = HCF(49,15) = HCF(64,49) = HCF(113,64) = HCF(516,113) .

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

Step 1: Since 514 > 1, we apply the division lemma to 514 and 1, to get

514 = 1 x 514 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 514 is 1

Notice that 1 = HCF(514,1) .

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Frequently Asked Questions on HCF of 113, 516, 514 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 113, 516, 514?

Answer: HCF of 113, 516, 514 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 113, 516, 514 using Euclid's Algorithm?

Answer: For arbitrary numbers 113, 516, 514 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.