Highest Common Factor of 312, 215, 196 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 312, 215, 196 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 312, 215, 196 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 312, 215, 196 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 312, 215, 196 is 1.

HCF(312, 215, 196) = 1

HCF of 312, 215, 196 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 312, 215, 196 is 1.

Highest Common Factor of 312,215,196 using Euclid's algorithm

Highest Common Factor of 312,215,196 is 1

Step 1: Since 312 > 215, we apply the division lemma to 312 and 215, to get

312 = 215 x 1 + 97

Step 2: Since the reminder 215 ≠ 0, we apply division lemma to 97 and 215, to get

215 = 97 x 2 + 21

Step 3: We consider the new divisor 97 and the new remainder 21, and apply the division lemma to get

97 = 21 x 4 + 13

We consider the new divisor 21 and the new remainder 13,and apply the division lemma to get

21 = 13 x 1 + 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 312 and 215 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(13,8) = HCF(21,13) = HCF(97,21) = HCF(215,97) = HCF(312,215) .

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

Step 1: Since 196 > 1, we apply the division lemma to 196 and 1, to get

196 = 1 x 196 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 196 is 1

Notice that 1 = HCF(196,1) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 312, 215, 196 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 312, 215, 196?

Answer: HCF of 312, 215, 196 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 312, 215, 196 using Euclid's Algorithm?

Answer: For arbitrary numbers 312, 215, 196 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.