Highest Common Factor of 729, 7798 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, 7798 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 729, 7798 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, 7798 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, 7798 is 1.

HCF(729, 7798) = 1

HCF of 729, 7798 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, 7798 is 1.

Highest Common Factor of 729,7798 using Euclid's algorithm

Highest Common Factor of 729,7798 is 1

Step 1: Since 7798 > 729, we apply the division lemma to 7798 and 729, to get

7798 = 729 x 10 + 508

Step 2: Since the reminder 729 ≠ 0, we apply division lemma to 508 and 729, to get

729 = 508 x 1 + 221

Step 3: We consider the new divisor 508 and the new remainder 221, and apply the division lemma to get

508 = 221 x 2 + 66

We consider the new divisor 221 and the new remainder 66,and apply the division lemma to get

221 = 66 x 3 + 23

We consider the new divisor 66 and the new remainder 23,and apply the division lemma to get

66 = 23 x 2 + 20

We consider the new divisor 23 and the new remainder 20,and apply the division lemma to get

23 = 20 x 1 + 3

We consider the new divisor 20 and the new remainder 3,and apply the division lemma to get

20 = 3 x 6 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 729 and 7798 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(20,3) = HCF(23,20) = HCF(66,23) = HCF(221,66) = HCF(508,221) = HCF(729,508) = HCF(7798,729) .

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Frequently Asked Questions on HCF of 729, 7798 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, 7798?

Answer: HCF of 729, 7798 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 729, 7798 using Euclid's Algorithm?

Answer: For arbitrary numbers 729, 7798 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.