Highest Common Factor of 614, 212, 226 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 614, 212, 226 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 614, 212, 226 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 614, 212, 226 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 614, 212, 226 is 2.

HCF(614, 212, 226) = 2

HCF of 614, 212, 226 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 614, 212, 226 is 2.

Highest Common Factor of 614,212,226 using Euclid's algorithm

Highest Common Factor of 614,212,226 is 2

Step 1: Since 614 > 212, we apply the division lemma to 614 and 212, to get

614 = 212 x 2 + 190

Step 2: Since the reminder 212 ≠ 0, we apply division lemma to 190 and 212, to get

212 = 190 x 1 + 22

Step 3: We consider the new divisor 190 and the new remainder 22, and apply the division lemma to get

190 = 22 x 8 + 14

We consider the new divisor 22 and the new remainder 14,and apply the division lemma to get

22 = 14 x 1 + 8

We consider the new divisor 14 and the new remainder 8,and apply the division lemma to get

14 = 8 x 1 + 6

We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get

8 = 6 x 1 + 2

We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get

6 = 2 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 614 and 212 is 2

Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(14,8) = HCF(22,14) = HCF(190,22) = HCF(212,190) = HCF(614,212) .

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

Step 1: Since 226 > 2, we apply the division lemma to 226 and 2, to get

226 = 2 x 113 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 226 is 2

Notice that 2 = HCF(226,2) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 614, 212, 226 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 614, 212, 226?

Answer: HCF of 614, 212, 226 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 614, 212, 226 using Euclid's Algorithm?

Answer: For arbitrary numbers 614, 212, 226 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.