Highest Common Factor of 212, 517, 130 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 212, 517, 130 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 212, 517, 130 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 212, 517, 130 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 212, 517, 130 is 1.

HCF(212, 517, 130) = 1

HCF of 212, 517, 130 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 212, 517, 130 is 1.

Highest Common Factor of 212,517,130 using Euclid's algorithm

Highest Common Factor of 212,517,130 is 1

Step 1: Since 517 > 212, we apply the division lemma to 517 and 212, to get

517 = 212 x 2 + 93

Step 2: Since the reminder 212 ≠ 0, we apply division lemma to 93 and 212, to get

212 = 93 x 2 + 26

Step 3: We consider the new divisor 93 and the new remainder 26, and apply the division lemma to get

93 = 26 x 3 + 15

We consider the new divisor 26 and the new remainder 15,and apply the division lemma to get

26 = 15 x 1 + 11

We consider the new divisor 15 and the new remainder 11,and apply the division lemma to get

15 = 11 x 1 + 4

We consider the new divisor 11 and the new remainder 4,and apply the division lemma to get

11 = 4 x 2 + 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 212 and 517 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(11,4) = HCF(15,11) = HCF(26,15) = HCF(93,26) = HCF(212,93) = HCF(517,212) .

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

Step 1: Since 130 > 1, we apply the division lemma to 130 and 1, to get

130 = 1 x 130 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 130 is 1

Notice that 1 = HCF(130,1) .

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Frequently Asked Questions on HCF of 212, 517, 130 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 212, 517, 130?

Answer: HCF of 212, 517, 130 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 212, 517, 130 using Euclid's Algorithm?

Answer: For arbitrary numbers 212, 517, 130 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.