Highest Common Factor of 316, 585, 840 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, 585, 840 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 316, 585, 840 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, 585, 840 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, 585, 840 is 1.

HCF(316, 585, 840) = 1

HCF of 316, 585, 840 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, 585, 840 is 1.

Highest Common Factor of 316,585,840 using Euclid's algorithm

Highest Common Factor of 316,585,840 is 1

Step 1: Since 585 > 316, we apply the division lemma to 585 and 316, to get

585 = 316 x 1 + 269

Step 2: Since the reminder 316 ≠ 0, we apply division lemma to 269 and 316, to get

316 = 269 x 1 + 47

Step 3: We consider the new divisor 269 and the new remainder 47, and apply the division lemma to get

269 = 47 x 5 + 34

We consider the new divisor 47 and the new remainder 34,and apply the division lemma to get

47 = 34 x 1 + 13

We consider the new divisor 34 and the new remainder 13,and apply the division lemma to get

34 = 13 x 2 + 8

We consider the new divisor 13 and the new remainder 8,and apply the division lemma to get

13 = 8 x 1 + 5

We consider the new divisor 8 and the new remainder 5,and apply the division lemma to get

8 = 5 x 1 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 316 and 585 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(13,8) = HCF(34,13) = HCF(47,34) = HCF(269,47) = HCF(316,269) = HCF(585,316) .

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

Step 1: Since 840 > 1, we apply the division lemma to 840 and 1, to get

840 = 1 x 840 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 840 is 1

Notice that 1 = HCF(840,1) .

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Frequently Asked Questions on HCF of 316, 585, 840 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, 585, 840?

Answer: HCF of 316, 585, 840 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 316, 585, 840 using Euclid's Algorithm?

Answer: For arbitrary numbers 316, 585, 840 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.