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GCF of 109/30, 288/375

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 109/30, 288/375 i.e 1/750 easily. The following is the detailed procedure to determine the greatest common factor of fractions 109/30, 288/375.

Enter two or more fractions separated by "commas"

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

GCF of:

What is the GCF of 109/30,288/375?

Given fractions are 109/30,288/375

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 109/30,288/375, numerators are 109,288

Denominators are 30,375

The GCF of 109,288 is 1 .

LCM of 30,375 is 750.

The greatest common factor of 109/30,288/375 = [GCF of 109,288]/[LCM of 30,375]= 1/750

Therefore, the GCF of 109/30,288/375 is 1/750.

Greatest Common Factor of 109,288

To find the highest common factor of 109,288, we have to find the factors of both numbers and list the highest common factor.

The factors of 109 are 1, 109

The factors of 288 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 288

The HCF of 109,288 is 1.

Lets's calculate GCF of 109,288

Greatest Common Factor (GCF) of 109,288 By Common Division

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

Greatest Common Factor of 109,288 By Matching Biggest Common Factor Method

Greatest Common Factor of 109,288 By Matching Biggest Common Factor Method

Now, list down the factors of 109

:

1,109

Now, list down the factors of 288

:

1,2,3,4,6,8,9,12,16,18,24,32,36,48,72,96,144,288

Greatest Common Factor

We found the factors 109,288 . The biggest common factor number is the GCF number.
So the greatest common factor 109,288 is 1.

Lets's calculate LCM of 30,375

Lowest Common Multiple of 30,375 using Common Division

3 30, 375
5 10, 125
2, 25

∴ So the LCM of the given numbers is 3 x 5 x 2 x 25 = 750

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/750

Therefore, the GCF of Fractions 109/30,288/375 is 1/750

Least Common Multiple of 30,375 with GCF Formula

Least Common Multiple of 30,375 with GCF Formula

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

We need to calculate greatest common factor of 30,375 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(30,375) = 15

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

GCF(30,375) x common factors =15 x 1 = 15

LCM(30,375) = ( 30 × 375 ) / 15

LCM(30,375) = 11250 / 15

LCM(30,375) = 750


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FAQs on GCF of Fractions of 109/30, 288/375

1. What is the HCF of 109,288?

The HCF of 109,288 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 109/30, 288/375?

Answer: GCF of Numerators as per given numbers 109/30, 288/375 is

GCF of Numerators i.e. for 109,288 is 1

LCM of denominators i.e. for 30,375 is 750.

Thus, GCF of Fractions is 1/750.Finally, GCF of Fractions for 109/30, 288/375 is 1/750.