Highest Common Factor of 183, 614, 564 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 183, 614, 564 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 183, 614, 564 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 183, 614, 564 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 183, 614, 564 is 1.

HCF(183, 614, 564) = 1

HCF of 183, 614, 564 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 183, 614, 564 is 1.

Highest Common Factor of 183,614,564 using Euclid's algorithm

Highest Common Factor of 183,614,564 is 1

Step 1: Since 614 > 183, we apply the division lemma to 614 and 183, to get

614 = 183 x 3 + 65

Step 2: Since the reminder 183 ≠ 0, we apply division lemma to 65 and 183, to get

183 = 65 x 2 + 53

Step 3: We consider the new divisor 65 and the new remainder 53, and apply the division lemma to get

65 = 53 x 1 + 12

We consider the new divisor 53 and the new remainder 12,and apply the division lemma to get

53 = 12 x 4 + 5

We consider the new divisor 12 and the new remainder 5,and apply the division lemma to get

12 = 5 x 2 + 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 183 and 614 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(12,5) = HCF(53,12) = HCF(65,53) = HCF(183,65) = HCF(614,183) .

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

Step 1: Since 564 > 1, we apply the division lemma to 564 and 1, to get

564 = 1 x 564 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 564 is 1

Notice that 1 = HCF(564,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 183, 614, 564 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 183, 614, 564?

Answer: HCF of 183, 614, 564 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 183, 614, 564 using Euclid's Algorithm?

Answer: For arbitrary numbers 183, 614, 564 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.