Highest Common Factor of 506, 311, 805 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, 311, 805 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 506, 311, 805 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, 311, 805 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, 311, 805 is 1.

HCF(506, 311, 805) = 1

HCF of 506, 311, 805 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, 311, 805 is 1.

Highest Common Factor of 506,311,805 using Euclid's algorithm

Highest Common Factor of 506,311,805 is 1

Step 1: Since 506 > 311, we apply the division lemma to 506 and 311, to get

506 = 311 x 1 + 195

Step 2: Since the reminder 311 ≠ 0, we apply division lemma to 195 and 311, to get

311 = 195 x 1 + 116

Step 3: We consider the new divisor 195 and the new remainder 116, and apply the division lemma to get

195 = 116 x 1 + 79

We consider the new divisor 116 and the new remainder 79,and apply the division lemma to get

116 = 79 x 1 + 37

We consider the new divisor 79 and the new remainder 37,and apply the division lemma to get

79 = 37 x 2 + 5

We consider the new divisor 37 and the new remainder 5,and apply the division lemma to get

37 = 5 x 7 + 2

We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get

5 = 2 x 2 + 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 506 and 311 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(37,5) = HCF(79,37) = HCF(116,79) = HCF(195,116) = HCF(311,195) = HCF(506,311) .

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

Step 1: Since 805 > 1, we apply the division lemma to 805 and 1, to get

805 = 1 x 805 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 805 is 1

Notice that 1 = HCF(805,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 506, 311, 805 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, 311, 805?

Answer: HCF of 506, 311, 805 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 506, 311, 805 using Euclid's Algorithm?

Answer: For arbitrary numbers 506, 311, 805 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.