Highest Common Factor of 310, 563 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 310, 563 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 310, 563 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 310, 563 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 310, 563 is 1.

HCF(310, 563) = 1

HCF of 310, 563 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 310, 563 is 1.

Highest Common Factor of 310,563 using Euclid's algorithm

Highest Common Factor of 310,563 is 1

Step 1: Since 563 > 310, we apply the division lemma to 563 and 310, to get

563 = 310 x 1 + 253

Step 2: Since the reminder 310 ≠ 0, we apply division lemma to 253 and 310, to get

310 = 253 x 1 + 57

Step 3: We consider the new divisor 253 and the new remainder 57, and apply the division lemma to get

253 = 57 x 4 + 25

We consider the new divisor 57 and the new remainder 25,and apply the division lemma to get

57 = 25 x 2 + 7

We consider the new divisor 25 and the new remainder 7,and apply the division lemma to get

25 = 7 x 3 + 4

We consider the new divisor 7 and the new remainder 4,and apply the division lemma to get

7 = 4 x 1 + 3

We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get

4 = 3 x 1 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 310 and 563 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(7,4) = HCF(25,7) = HCF(57,25) = HCF(253,57) = HCF(310,253) = HCF(563,310) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 310, 563 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 310, 563?

Answer: HCF of 310, 563 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 310, 563 using Euclid's Algorithm?

Answer: For arbitrary numbers 310, 563 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.