Highest Common Factor of 310, 518, 165 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 310, 518, 165 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 310, 518, 165 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 310, 518, 165 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 310, 518, 165 is 1.

HCF(310, 518, 165) = 1

HCF of 310, 518, 165 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 310, 518, 165 is 1.

Highest Common Factor of 310,518,165 using Euclid's algorithm

Highest Common Factor of 310,518,165 is 1

Step 1: Since 518 > 310, we apply the division lemma to 518 and 310, to get

518 = 310 x 1 + 208

Step 2: Since the reminder 310 ≠ 0, we apply division lemma to 208 and 310, to get

310 = 208 x 1 + 102

Step 3: We consider the new divisor 208 and the new remainder 102, and apply the division lemma to get

208 = 102 x 2 + 4

We consider the new divisor 102 and the new remainder 4,and apply the division lemma to get

102 = 4 x 25 + 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 310 and 518 is 2

Notice that 2 = HCF(4,2) = HCF(102,4) = HCF(208,102) = HCF(310,208) = HCF(518,310) .

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

Step 1: Since 165 > 2, we apply the division lemma to 165 and 2, to get

165 = 2 x 82 + 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 165 is 1

Notice that 1 = HCF(2,1) = HCF(165,2) .

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Frequently Asked Questions on HCF of 310, 518, 165 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 310, 518, 165?

Answer: HCF of 310, 518, 165 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 310, 518, 165 using Euclid's Algorithm?

Answer: For arbitrary numbers 310, 518, 165 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.