Highest Common Factor of 720, 575, 729 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 720, 575, 729 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 720, 575, 729 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 720, 575, 729 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 720, 575, 729 is 1.

HCF(720, 575, 729) = 1

HCF of 720, 575, 729 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 720, 575, 729 is 1.

Highest Common Factor of 720,575,729 using Euclid's algorithm

Highest Common Factor of 720,575,729 is 1

Step 1: Since 720 > 575, we apply the division lemma to 720 and 575, to get

720 = 575 x 1 + 145

Step 2: Since the reminder 575 ≠ 0, we apply division lemma to 145 and 575, to get

575 = 145 x 3 + 140

Step 3: We consider the new divisor 145 and the new remainder 140, and apply the division lemma to get

145 = 140 x 1 + 5

We consider the new divisor 140 and the new remainder 5, and apply the division lemma to get

140 = 5 x 28 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 720 and 575 is 5

Notice that 5 = HCF(140,5) = HCF(145,140) = HCF(575,145) = HCF(720,575) .

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

Step 1: Since 729 > 5, we apply the division lemma to 729 and 5, to get

729 = 5 x 145 + 4

Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 4 and 5, to get

5 = 4 x 1 + 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 5 and 729 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(729,5) .

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Frequently Asked Questions on HCF of 720, 575, 729 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 720, 575, 729?

Answer: HCF of 720, 575, 729 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 720, 575, 729 using Euclid's Algorithm?

Answer: For arbitrary numbers 720, 575, 729 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.