Highest Common Factor of 315, 210, 986 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 315, 210, 986 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 315, 210, 986 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 315, 210, 986 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 315, 210, 986 is 1.

HCF(315, 210, 986) = 1

HCF of 315, 210, 986 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 315, 210, 986 is 1.

Highest Common Factor of 315,210,986 using Euclid's algorithm

Highest Common Factor of 315,210,986 is 1

Step 1: Since 315 > 210, we apply the division lemma to 315 and 210, to get

315 = 210 x 1 + 105

Step 2: Since the reminder 210 ≠ 0, we apply division lemma to 105 and 210, to get

210 = 105 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 105, the HCF of 315 and 210 is 105

Notice that 105 = HCF(210,105) = HCF(315,210) .

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

Step 1: Since 986 > 105, we apply the division lemma to 986 and 105, to get

986 = 105 x 9 + 41

Step 2: Since the reminder 105 ≠ 0, we apply division lemma to 41 and 105, to get

105 = 41 x 2 + 23

Step 3: We consider the new divisor 41 and the new remainder 23, and apply the division lemma to get

41 = 23 x 1 + 18

We consider the new divisor 23 and the new remainder 18,and apply the division lemma to get

23 = 18 x 1 + 5

We consider the new divisor 18 and the new remainder 5,and apply the division lemma to get

18 = 5 x 3 + 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 105 and 986 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(18,5) = HCF(23,18) = HCF(41,23) = HCF(105,41) = HCF(986,105) .

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Frequently Asked Questions on HCF of 315, 210, 986 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 315, 210, 986?

Answer: HCF of 315, 210, 986 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 315, 210, 986 using Euclid's Algorithm?

Answer: For arbitrary numbers 315, 210, 986 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.