Highest Common Factor of 195, 364, 14 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 195, 364, 14 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 195, 364, 14 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 195, 364, 14 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 195, 364, 14 is 1.

HCF(195, 364, 14) = 1

HCF of 195, 364, 14 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 195, 364, 14 is 1.

Highest Common Factor of 195,364,14 using Euclid's algorithm

Highest Common Factor of 195,364,14 is 1

Step 1: Since 364 > 195, we apply the division lemma to 364 and 195, to get

364 = 195 x 1 + 169

Step 2: Since the reminder 195 ≠ 0, we apply division lemma to 169 and 195, to get

195 = 169 x 1 + 26

Step 3: We consider the new divisor 169 and the new remainder 26, and apply the division lemma to get

169 = 26 x 6 + 13

We consider the new divisor 26 and the new remainder 13, and apply the division lemma to get

26 = 13 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 13, the HCF of 195 and 364 is 13

Notice that 13 = HCF(26,13) = HCF(169,26) = HCF(195,169) = HCF(364,195) .

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

Step 1: Since 14 > 13, we apply the division lemma to 14 and 13, to get

14 = 13 x 1 + 1

Step 2: Since the reminder 13 ≠ 0, we apply division lemma to 1 and 13, to get

13 = 1 x 13 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 13 and 14 is 1

Notice that 1 = HCF(13,1) = HCF(14,13) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 195, 364, 14 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 195, 364, 14?

Answer: HCF of 195, 364, 14 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 195, 364, 14 using Euclid's Algorithm?

Answer: For arbitrary numbers 195, 364, 14 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.