Highest Common Factor of 506, 326, 316 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 506, 326, 316 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 506, 326, 316 is 2 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 506, 326, 316 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 506, 326, 316 is 2.

HCF(506, 326, 316) = 2

HCF of 506, 326, 316 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 506, 326, 316 is 2.

Highest Common Factor of 506,326,316 using Euclid's algorithm

Highest Common Factor of 506,326,316 is 2

Step 1: Since 506 > 326, we apply the division lemma to 506 and 326, to get

506 = 326 x 1 + 180

Step 2: Since the reminder 326 ≠ 0, we apply division lemma to 180 and 326, to get

326 = 180 x 1 + 146

Step 3: We consider the new divisor 180 and the new remainder 146, and apply the division lemma to get

180 = 146 x 1 + 34

We consider the new divisor 146 and the new remainder 34,and apply the division lemma to get

146 = 34 x 4 + 10

We consider the new divisor 34 and the new remainder 10,and apply the division lemma to get

34 = 10 x 3 + 4

We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get

10 = 4 x 2 + 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 506 and 326 is 2

Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(34,10) = HCF(146,34) = HCF(180,146) = HCF(326,180) = HCF(506,326) .

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

Step 1: Since 316 > 2, we apply the division lemma to 316 and 2, to get

316 = 2 x 158 + 0

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

Notice that 2 = HCF(316,2) .

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Frequently Asked Questions on HCF of 506, 326, 316 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 506, 326, 316?

Answer: HCF of 506, 326, 316 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 506, 326, 316 using Euclid's Algorithm?

Answer: For arbitrary numbers 506, 326, 316 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.