Highest Common Factor of 412, 174, 394 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 412, 174, 394 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 412, 174, 394 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 412, 174, 394 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 412, 174, 394 is 2.

HCF(412, 174, 394) = 2

HCF of 412, 174, 394 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 412, 174, 394 is 2.

Highest Common Factor of 412,174,394 using Euclid's algorithm

Highest Common Factor of 412,174,394 is 2

Step 1: Since 412 > 174, we apply the division lemma to 412 and 174, to get

412 = 174 x 2 + 64

Step 2: Since the reminder 174 ≠ 0, we apply division lemma to 64 and 174, to get

174 = 64 x 2 + 46

Step 3: We consider the new divisor 64 and the new remainder 46, and apply the division lemma to get

64 = 46 x 1 + 18

We consider the new divisor 46 and the new remainder 18,and apply the division lemma to get

46 = 18 x 2 + 10

We consider the new divisor 18 and the new remainder 10,and apply the division lemma to get

18 = 10 x 1 + 8

We consider the new divisor 10 and the new remainder 8,and apply the division lemma to get

10 = 8 x 1 + 2

We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get

8 = 2 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 412 and 174 is 2

Notice that 2 = HCF(8,2) = HCF(10,8) = HCF(18,10) = HCF(46,18) = HCF(64,46) = HCF(174,64) = HCF(412,174) .

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

Step 1: Since 394 > 2, we apply the division lemma to 394 and 2, to get

394 = 2 x 197 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 394 is 2

Notice that 2 = HCF(394,2) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 412, 174, 394 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 412, 174, 394?

Answer: HCF of 412, 174, 394 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 412, 174, 394 using Euclid's Algorithm?

Answer: For arbitrary numbers 412, 174, 394 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.