Highest Common Factor of 506, 728, 781 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 506, 728, 781 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 506, 728, 781 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 506, 728, 781 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 506, 728, 781 is 1.

HCF(506, 728, 781) = 1

HCF of 506, 728, 781 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 506, 728, 781 is 1.

Highest Common Factor of 506,728,781 using Euclid's algorithm

Highest Common Factor of 506,728,781 is 1

Step 1: Since 728 > 506, we apply the division lemma to 728 and 506, to get

728 = 506 x 1 + 222

Step 2: Since the reminder 506 ≠ 0, we apply division lemma to 222 and 506, to get

506 = 222 x 2 + 62

Step 3: We consider the new divisor 222 and the new remainder 62, and apply the division lemma to get

222 = 62 x 3 + 36

We consider the new divisor 62 and the new remainder 36,and apply the division lemma to get

62 = 36 x 1 + 26

We consider the new divisor 36 and the new remainder 26,and apply the division lemma to get

36 = 26 x 1 + 10

We consider the new divisor 26 and the new remainder 10,and apply the division lemma to get

26 = 10 x 2 + 6

We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get

10 = 6 x 1 + 4

We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get

6 = 4 x 1 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 506 and 728 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(26,10) = HCF(36,26) = HCF(62,36) = HCF(222,62) = HCF(506,222) = HCF(728,506) .

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

Step 1: Since 781 > 2, we apply the division lemma to 781 and 2, to get

781 = 2 x 390 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 781 is 1

Notice that 1 = HCF(2,1) = HCF(781,2) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 506, 728, 781 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 506, 728, 781?

Answer: HCF of 506, 728, 781 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 506, 728, 781 using Euclid's Algorithm?

Answer: For arbitrary numbers 506, 728, 781 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.