Highest Common Factor of 563, 852 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 563, 852 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 563, 852 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 563, 852 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 563, 852 is 1.

HCF(563, 852) = 1

HCF of 563, 852 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 563, 852 is 1.

Highest Common Factor of 563,852 using Euclid's algorithm

Highest Common Factor of 563,852 is 1

Step 1: Since 852 > 563, we apply the division lemma to 852 and 563, to get

852 = 563 x 1 + 289

Step 2: Since the reminder 563 ≠ 0, we apply division lemma to 289 and 563, to get

563 = 289 x 1 + 274

Step 3: We consider the new divisor 289 and the new remainder 274, and apply the division lemma to get

289 = 274 x 1 + 15

We consider the new divisor 274 and the new remainder 15,and apply the division lemma to get

274 = 15 x 18 + 4

We consider the new divisor 15 and the new remainder 4,and apply the division lemma to get

15 = 4 x 3 + 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 563 and 852 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(15,4) = HCF(274,15) = HCF(289,274) = HCF(563,289) = HCF(852,563) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 563, 852 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 563, 852?

Answer: HCF of 563, 852 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 563, 852 using Euclid's Algorithm?

Answer: For arbitrary numbers 563, 852 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.