Highest Common Factor of 728, 195, 186 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 728, 195, 186 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 728, 195, 186 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 728, 195, 186 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 728, 195, 186 is 1.

HCF(728, 195, 186) = 1

HCF of 728, 195, 186 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 728, 195, 186 is 1.

Highest Common Factor of 728,195,186 using Euclid's algorithm

Highest Common Factor of 728,195,186 is 1

Step 1: Since 728 > 195, we apply the division lemma to 728 and 195, to get

728 = 195 x 3 + 143

Step 2: Since the reminder 195 ≠ 0, we apply division lemma to 143 and 195, to get

195 = 143 x 1 + 52

Step 3: We consider the new divisor 143 and the new remainder 52, and apply the division lemma to get

143 = 52 x 2 + 39

We consider the new divisor 52 and the new remainder 39,and apply the division lemma to get

52 = 39 x 1 + 13

We consider the new divisor 39 and the new remainder 13,and apply the division lemma to get

39 = 13 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 13, the HCF of 728 and 195 is 13

Notice that 13 = HCF(39,13) = HCF(52,39) = HCF(143,52) = HCF(195,143) = HCF(728,195) .

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

Step 1: Since 186 > 13, we apply the division lemma to 186 and 13, to get

186 = 13 x 14 + 4

Step 2: Since the reminder 13 ≠ 0, we apply division lemma to 4 and 13, to get

13 = 4 x 3 + 1

Step 3: We consider the new divisor 4 and the new remainder 1, and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 13 and 186 is 1

Notice that 1 = HCF(4,1) = HCF(13,4) = HCF(186,13) .

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Frequently Asked Questions on HCF of 728, 195, 186 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 728, 195, 186?

Answer: HCF of 728, 195, 186 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 728, 195, 186 using Euclid's Algorithm?

Answer: For arbitrary numbers 728, 195, 186 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.