Highest Common Factor of 505, 860, 728 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 505, 860, 728 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 505, 860, 728 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 505, 860, 728 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 505, 860, 728 is 1.

HCF(505, 860, 728) = 1

HCF of 505, 860, 728 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 505, 860, 728 is 1.

Highest Common Factor of 505,860,728 using Euclid's algorithm

Highest Common Factor of 505,860,728 is 1

Step 1: Since 860 > 505, we apply the division lemma to 860 and 505, to get

860 = 505 x 1 + 355

Step 2: Since the reminder 505 ≠ 0, we apply division lemma to 355 and 505, to get

505 = 355 x 1 + 150

Step 3: We consider the new divisor 355 and the new remainder 150, and apply the division lemma to get

355 = 150 x 2 + 55

We consider the new divisor 150 and the new remainder 55,and apply the division lemma to get

150 = 55 x 2 + 40

We consider the new divisor 55 and the new remainder 40,and apply the division lemma to get

55 = 40 x 1 + 15

We consider the new divisor 40 and the new remainder 15,and apply the division lemma to get

40 = 15 x 2 + 10

We consider the new divisor 15 and the new remainder 10,and apply the division lemma to get

15 = 10 x 1 + 5

We consider the new divisor 10 and the new remainder 5,and apply the division lemma to get

10 = 5 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 505 and 860 is 5

Notice that 5 = HCF(10,5) = HCF(15,10) = HCF(40,15) = HCF(55,40) = HCF(150,55) = HCF(355,150) = HCF(505,355) = HCF(860,505) .

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

Step 1: Since 728 > 5, we apply the division lemma to 728 and 5, to get

728 = 5 x 145 + 3

Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 3 and 5, to get

5 = 3 x 1 + 2

Step 3: 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 5 and 728 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(728,5) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 505, 860, 728 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 505, 860, 728?

Answer: HCF of 505, 860, 728 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 505, 860, 728 using Euclid's Algorithm?

Answer: For arbitrary numbers 505, 860, 728 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.