Highest Common Factor of 729, 916, 13 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 729, 916, 13 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 729, 916, 13 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 729, 916, 13 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 729, 916, 13 is 1.

HCF(729, 916, 13) = 1

HCF of 729, 916, 13 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 729, 916, 13 is 1.

Highest Common Factor of 729,916,13 using Euclid's algorithm

Highest Common Factor of 729,916,13 is 1

Step 1: Since 916 > 729, we apply the division lemma to 916 and 729, to get

916 = 729 x 1 + 187

Step 2: Since the reminder 729 ≠ 0, we apply division lemma to 187 and 729, to get

729 = 187 x 3 + 168

Step 3: We consider the new divisor 187 and the new remainder 168, and apply the division lemma to get

187 = 168 x 1 + 19

We consider the new divisor 168 and the new remainder 19,and apply the division lemma to get

168 = 19 x 8 + 16

We consider the new divisor 19 and the new remainder 16,and apply the division lemma to get

19 = 16 x 1 + 3

We consider the new divisor 16 and the new remainder 3,and apply the division lemma to get

16 = 3 x 5 + 1

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

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 729 and 916 is 1

Notice that 1 = HCF(3,1) = HCF(16,3) = HCF(19,16) = HCF(168,19) = HCF(187,168) = HCF(729,187) = HCF(916,729) .

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

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

Notice that 1 = HCF(13,1) .

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Frequently Asked Questions on HCF of 729, 916, 13 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 729, 916, 13?

Answer: HCF of 729, 916, 13 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 729, 916, 13 using Euclid's Algorithm?

Answer: For arbitrary numbers 729, 916, 13 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.