Highest Common Factor of 518, 316, 357 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 518, 316, 357 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 518, 316, 357 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 518, 316, 357 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 518, 316, 357 is 1.

HCF(518, 316, 357) = 1

HCF of 518, 316, 357 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 518, 316, 357 is 1.

Highest Common Factor of 518,316,357 using Euclid's algorithm

Highest Common Factor of 518,316,357 is 1

Step 1: Since 518 > 316, we apply the division lemma to 518 and 316, to get

518 = 316 x 1 + 202

Step 2: Since the reminder 316 ≠ 0, we apply division lemma to 202 and 316, to get

316 = 202 x 1 + 114

Step 3: We consider the new divisor 202 and the new remainder 114, and apply the division lemma to get

202 = 114 x 1 + 88

We consider the new divisor 114 and the new remainder 88,and apply the division lemma to get

114 = 88 x 1 + 26

We consider the new divisor 88 and the new remainder 26,and apply the division lemma to get

88 = 26 x 3 + 10

We consider the new divisor 26 and the new remainder 10,and apply the division lemma to get

26 = 10 x 2 + 6

We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get

10 = 6 x 1 + 4

We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get

6 = 4 x 1 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 518 and 316 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(26,10) = HCF(88,26) = HCF(114,88) = HCF(202,114) = HCF(316,202) = HCF(518,316) .

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

Step 1: Since 357 > 2, we apply the division lemma to 357 and 2, to get

357 = 2 x 178 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 357 is 1

Notice that 1 = HCF(2,1) = HCF(357,2) .

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Frequently Asked Questions on HCF of 518, 316, 357 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 518, 316, 357?

Answer: HCF of 518, 316, 357 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 518, 316, 357 using Euclid's Algorithm?

Answer: For arbitrary numbers 518, 316, 357 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.