Highest Common Factor of 731, 1725 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 731, 1725 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 731, 1725 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 731, 1725 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 731, 1725 is 1.

HCF(731, 1725) = 1

HCF of 731, 1725 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 731, 1725 is 1.

Highest Common Factor of 731,1725 using Euclid's algorithm

Highest Common Factor of 731,1725 is 1

Step 1: Since 1725 > 731, we apply the division lemma to 1725 and 731, to get

1725 = 731 x 2 + 263

Step 2: Since the reminder 731 ≠ 0, we apply division lemma to 263 and 731, to get

731 = 263 x 2 + 205

Step 3: We consider the new divisor 263 and the new remainder 205, and apply the division lemma to get

263 = 205 x 1 + 58

We consider the new divisor 205 and the new remainder 58,and apply the division lemma to get

205 = 58 x 3 + 31

We consider the new divisor 58 and the new remainder 31,and apply the division lemma to get

58 = 31 x 1 + 27

We consider the new divisor 31 and the new remainder 27,and apply the division lemma to get

31 = 27 x 1 + 4

We consider the new divisor 27 and the new remainder 4,and apply the division lemma to get

27 = 4 x 6 + 3

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

4 = 3 x 1 + 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 731 and 1725 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(27,4) = HCF(31,27) = HCF(58,31) = HCF(205,58) = HCF(263,205) = HCF(731,263) = HCF(1725,731) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 731, 1725 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 731, 1725?

Answer: HCF of 731, 1725 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 731, 1725 using Euclid's Algorithm?

Answer: For arbitrary numbers 731, 1725 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.