Highest Common Factor of 516, 299, 119 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 516, 299, 119 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 516, 299, 119 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 516, 299, 119 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 516, 299, 119 is 1.

HCF(516, 299, 119) = 1

HCF of 516, 299, 119 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 516, 299, 119 is 1.

Highest Common Factor of 516,299,119 using Euclid's algorithm

Highest Common Factor of 516,299,119 is 1

Step 1: Since 516 > 299, we apply the division lemma to 516 and 299, to get

516 = 299 x 1 + 217

Step 2: Since the reminder 299 ≠ 0, we apply division lemma to 217 and 299, to get

299 = 217 x 1 + 82

Step 3: We consider the new divisor 217 and the new remainder 82, and apply the division lemma to get

217 = 82 x 2 + 53

We consider the new divisor 82 and the new remainder 53,and apply the division lemma to get

82 = 53 x 1 + 29

We consider the new divisor 53 and the new remainder 29,and apply the division lemma to get

53 = 29 x 1 + 24

We consider the new divisor 29 and the new remainder 24,and apply the division lemma to get

29 = 24 x 1 + 5

We consider the new divisor 24 and the new remainder 5,and apply the division lemma to get

24 = 5 x 4 + 4

We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get

5 = 4 x 1 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 516 and 299 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(24,5) = HCF(29,24) = HCF(53,29) = HCF(82,53) = HCF(217,82) = HCF(299,217) = HCF(516,299) .

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

Step 1: Since 119 > 1, we apply the division lemma to 119 and 1, to get

119 = 1 x 119 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 119 is 1

Notice that 1 = HCF(119,1) .

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Frequently Asked Questions on HCF of 516, 299, 119 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 516, 299, 119?

Answer: HCF of 516, 299, 119 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 516, 299, 119 using Euclid's Algorithm?

Answer: For arbitrary numbers 516, 299, 119 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.