How to Find GCF of 540/582, 544/107?

GCF of 540/582, 544/107

Created By : Veerendra
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023

Use our free GCF of Fractions Calculator tool to compute the GCF of 540/582, 544/107 i.e 4/62274 easily. The following is the detailed procedure to determine the greatest common factor of fractions 540/582, 544/107.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

What is the GCF of 540/582,544/107?

Given fractions are 540/582,544/107

To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by

GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators

In the fractions 540/582,544/107, numerators are 540,544

Denominators are 582,107

The GCF of 540,544 is 4 .

LCM of 582,107 is 62274.

The greatest common factor of 540/582,544/107 = [GCF of 540,544]/[LCM of 582,107]= 4/62274

Therefore, the GCF of 540/582,544/107 is 4/62274.

Greatest Common Factor of 540,544

To find the highest common factor of 540,544, we have to find the factors of both numbers and list the highest common factor.

The factors of 540 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 90, 108, 135, 180, 270, 540

The factors of 544 are 1, 2, 4, 8, 16, 17, 32, 34, 68, 136, 272, 544

The HCF of 540,544 is 4.

Lets's calculate GCF of 540,544

Greatest Common Factor (GCF) of 540,544 By Common Division

2	540, 544
2	270, 272
	135, 136

∴ So the GCF of the given numbers is 2 x 2 = 4

Greatest Common Factor of 540,544 By Matching Biggest Common Factor Method

Now, list down the factors of 540

1,2,3,4,5,6,9,10,12,15,18,20,27,30,36,45,54,60,90,108,135,180,270,540

Now, list down the factors of 544

1,2,4,8,16,17,32,34,68,136,272,544

Greatest Common Factor

We found the factors 540,544 . The biggest common factor number is the GCF number.
So the greatest common factor 540,544 is 4.

Lets's calculate LCM of 582,107

Lowest Common Multiple of 582,107 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 62274

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/62274

Therefore, the GCF of Fractions 540/582,544/107 is 4/62274

Least Common Multiple of 582,107 with GCF Formula

The formula of LCM is LCM(a₁,a₂,a₃....,a_n) = ( a₁ × a₂ × a₃ × .... × a_n) / GCF(a₁,a₂,a₃....,a_n) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 582,107 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(582,107) = 1

common factors(in case of two or more numbers have common factors) = 1

GCF(582,107) x common factors =1 x 1 = 1

LCM(582,107) = ( 582 × 107 ) / 1

LCM(582,107) = 62274 / 1

LCM(582,107) = 62274

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 540/582, 544/107

1. What is the HCF of 540,544?

The HCF of 540,544 is 4

2. What is the GCF of a fraction?

The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.

3. How to find GCF in Fractions?

Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.

4. What is the GCF of Fractions for 540/582, 544/107?

Answer: GCF of Numerators as per given numbers 540/582, 544/107 is

GCF of Numerators i.e. for 540,544 is 4

LCM of denominators i.e. for 582,107 is 62274.

Thus, GCF of Fractions is 4/62274.Finally, GCF of Fractions for 540/582, 544/107 is 4/62274.