How to Find GCF of 15/45, 345/50, 509/108?

GCF of 15/45, 345/50, 509/108

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 15/45, 345/50, 509/108 i.e 1/2700 easily. The following is the detailed procedure to determine the greatest common factor of fractions 15/45, 345/50, 509/108.

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 15/45,345/50,509/108?

Given fractions are 15/45,345/50,509/108

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 15/45,345/50,509/108, numerators are 15,345,509

Denominators are 45,50,108

The GCF of 15,345,509 is 1 .

LCM of 45,50,108 is 2700.

The greatest common factor of 15/45,345/50,509/108 = [GCF of 15,345,509]/[LCM of 45,50,108]= 1/2700

Therefore, the GCF of 15/45,345/50,509/108 is 1/2700.

Greatest Common Factor of 15,345,509

To find the highest common factor of 15,345,509, we have to find the factors of both numbers and list the highest common factor.

The factors of 15 are 1, 3, 5, 15

The factors of 345 are 1, 3, 5, 15, 23, 69, 115, 345

The factors of 509 are 1, 509

The HCF of 15,345,509 is 1.

Lets's calculate GCF of 15,345,509

Greatest Common Factor (GCF) of 15,345,509 By Common Division

∴ So GCF of numbers is 1 because of no common factors present between them.

Greatest Common Factor of 15,345,509 By Matching Biggest Common Factor Method

Now, list down the factors of 15

1,3,5,15

Now, list down the factors of 345

1,3,5,15,23,69,115,345

Now, list down the factors of 509

1,509

Greatest Common Factor

We found the factors 15,345,509 . The biggest common factor number is the GCF number.
So the greatest common factor 15,345,509 is 1.

Lets's calculate LCM of 45,50,108

Lowest Common Multiple of 45,50,108 using Common Division

2	45, 50, 108
3	45, 25, 54
3	15, 25, 18
5	5, 25, 6
	1, 5, 6

∴ So the LCM of the given numbers is 2 x 3 x 3 x 5 x 1 x 5 x 6 = 2700

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2700

Therefore, the GCF of Fractions 15/45,345/50,509/108 is 1/2700

Least Common Multiple of 45,50,108 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 45,50,108 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(45,50,108) = 1

common factors(in case of two or more numbers have common factors) = 90

GCF(45,50,108) x common factors =1 x 90 = 90

LCM(45,50,108) = ( 45 × 50 × 108 ) / 90

LCM(45,50,108) = 243000 / 90

LCM(45,50,108) = 2700

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 15/45, 345/50, 509/108

1. What is the HCF of 15,345,509?

The HCF of 15,345,509 is 1

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 15/45, 345/50, 509/108?

Answer: GCF of Numerators as per given numbers 15/45, 345/50, 509/108 is

GCF of Numerators i.e. for 15,345,509 is 1

LCM of denominators i.e. for 45,50,108 is 2700.

Thus, GCF of Fractions is 1/2700.Finally, GCF of Fractions for 15/45, 345/50, 509/108 is 1/2700.