Highest Common Factor of 316, 517, 100 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 316, 517, 100 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 316, 517, 100 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 316, 517, 100 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 316, 517, 100 is 1.

HCF(316, 517, 100) = 1

HCF of 316, 517, 100 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 316, 517, 100 is 1.

Highest Common Factor of 316,517,100 using Euclid's algorithm

Highest Common Factor of 316,517,100 is 1

Step 1: Since 517 > 316, we apply the division lemma to 517 and 316, to get

517 = 316 x 1 + 201

Step 2: Since the reminder 316 ≠ 0, we apply division lemma to 201 and 316, to get

316 = 201 x 1 + 115

Step 3: We consider the new divisor 201 and the new remainder 115, and apply the division lemma to get

201 = 115 x 1 + 86

We consider the new divisor 115 and the new remainder 86,and apply the division lemma to get

115 = 86 x 1 + 29

We consider the new divisor 86 and the new remainder 29,and apply the division lemma to get

86 = 29 x 2 + 28

We consider the new divisor 29 and the new remainder 28,and apply the division lemma to get

29 = 28 x 1 + 1

We consider the new divisor 28 and the new remainder 1,and apply the division lemma to get

28 = 1 x 28 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 316 and 517 is 1

Notice that 1 = HCF(28,1) = HCF(29,28) = HCF(86,29) = HCF(115,86) = HCF(201,115) = HCF(316,201) = HCF(517,316) .

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

Step 1: Since 100 > 1, we apply the division lemma to 100 and 1, to get

100 = 1 x 100 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 100 is 1

Notice that 1 = HCF(100,1) .

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Frequently Asked Questions on HCF of 316, 517, 100 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 316, 517, 100?

Answer: HCF of 316, 517, 100 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 316, 517, 100 using Euclid's Algorithm?

Answer: For arbitrary numbers 316, 517, 100 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.