How to Find GCF of 28/48, 31/17, 469/53?

GCF of 28/48, 31/17, 469/53

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 28/48, 31/17, 469/53 i.e 1/43248 easily. The following is the detailed procedure to determine the greatest common factor of fractions 28/48, 31/17, 469/53.

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 28/48,31/17,469/53?

Given fractions are 28/48,31/17,469/53

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 28/48,31/17,469/53, numerators are 28,31,469

Denominators are 48,17,53

The GCF of 28,31,469 is 1 .

LCM of 48,17,53 is 43248.

The greatest common factor of 28/48,31/17,469/53 = [GCF of 28,31,469]/[LCM of 48,17,53]= 1/43248

Therefore, the GCF of 28/48,31/17,469/53 is 1/43248.

Greatest Common Factor of 28,31,469

To find the highest common factor of 28,31,469, we have to find the factors of both numbers and list the highest common factor.

The factors of 28 are 1, 2, 4, 7, 14, 28

The factors of 31 are 1, 31

The factors of 469 are 1, 7, 67, 469

The HCF of 28,31,469 is 1.

Lets's calculate GCF of 28,31,469

Greatest Common Factor (GCF) of 28,31,469 By Common Division

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

Greatest Common Factor of 28,31,469 By Matching Biggest Common Factor Method

Now, list down the factors of 28

1,2,4,7,14,28

Now, list down the factors of 31

1,31

Now, list down the factors of 469

1,7,67,469

Greatest Common Factor

We found the factors 28,31,469 . The biggest common factor number is the GCF number.
So the greatest common factor 28,31,469 is 1.

Lets's calculate LCM of 48,17,53

Lowest Common Multiple of 48,17,53 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 43248

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/43248

Therefore, the GCF of Fractions 28/48,31/17,469/53 is 1/43248

Least Common Multiple of 48,17,53 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 48,17,53 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(48,17,53) = 1

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

GCF(48,17,53) x common factors =1 x 1 = 1

LCM(48,17,53) = ( 48 × 17 × 53 ) / 1

LCM(48,17,53) = 43248 / 1

LCM(48,17,53) = 43248

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FAQs on GCF of Fractions of 28/48, 31/17, 469/53

1. What is the HCF of 28,31,469?

The HCF of 28,31,469 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 28/48, 31/17, 469/53?

Answer: GCF of Numerators as per given numbers 28/48, 31/17, 469/53 is

GCF of Numerators i.e. for 28,31,469 is 1

LCM of denominators i.e. for 48,17,53 is 43248.

Thus, GCF of Fractions is 1/43248.Finally, GCF of Fractions for 28/48, 31/17, 469/53 is 1/43248.