Highest Common Factor of 512, 889, 721 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 512, 889, 721 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 512, 889, 721 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 512, 889, 721 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 512, 889, 721 is 1.

HCF(512, 889, 721) = 1

HCF of 512, 889, 721 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 512, 889, 721 is 1.

Highest Common Factor of 512,889,721 using Euclid's algorithm

Highest Common Factor of 512,889,721 is 1

Step 1: Since 889 > 512, we apply the division lemma to 889 and 512, to get

889 = 512 x 1 + 377

Step 2: Since the reminder 512 ≠ 0, we apply division lemma to 377 and 512, to get

512 = 377 x 1 + 135

Step 3: We consider the new divisor 377 and the new remainder 135, and apply the division lemma to get

377 = 135 x 2 + 107

We consider the new divisor 135 and the new remainder 107,and apply the division lemma to get

135 = 107 x 1 + 28

We consider the new divisor 107 and the new remainder 28,and apply the division lemma to get

107 = 28 x 3 + 23

We consider the new divisor 28 and the new remainder 23,and apply the division lemma to get

28 = 23 x 1 + 5

We consider the new divisor 23 and the new remainder 5,and apply the division lemma to get

23 = 5 x 4 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 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 512 and 889 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(23,5) = HCF(28,23) = HCF(107,28) = HCF(135,107) = HCF(377,135) = HCF(512,377) = HCF(889,512) .

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

Step 1: Since 721 > 1, we apply the division lemma to 721 and 1, to get

721 = 1 x 721 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 721 is 1

Notice that 1 = HCF(721,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 512, 889, 721 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 512, 889, 721?

Answer: HCF of 512, 889, 721 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 512, 889, 721 using Euclid's Algorithm?

Answer: For arbitrary numbers 512, 889, 721 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.