How to Find GCF of 272/64, 288/7409?

GCF of 272/64, 288/7409

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 272/64, 288/7409 i.e 16/474176 easily. The following is the detailed procedure to determine the greatest common factor of fractions 272/64, 288/7409.

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 272/64,288/7409?

Given fractions are 272/64,288/7409

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 272/64,288/7409, numerators are 272,288

Denominators are 64,7409

The GCF of 272,288 is 16 .

LCM of 64,7409 is 474176.

The greatest common factor of 272/64,288/7409 = [GCF of 272,288]/[LCM of 64,7409]= 16/474176

Therefore, the GCF of 272/64,288/7409 is 16/474176.

Greatest Common Factor of 272,288

To find the highest common factor of 272,288, we have to find the factors of both numbers and list the highest common factor.

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

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 272,288 is 16.

Lets's calculate GCF of 272,288

Greatest Common Factor (GCF) of 272,288 By Common Division

2	272, 288
2	136, 144
2	68, 72
2	34, 36
	17, 18

∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 = 16

Greatest Common Factor of 272,288 By Matching Biggest Common Factor Method

Now, list down the factors of 272

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

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 272,288 . The biggest common factor number is the GCF number.
So the greatest common factor 272,288 is 16.

Lets's calculate LCM of 64,7409

Lowest Common Multiple of 64,7409 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 474176

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 16/474176

Therefore, the GCF of Fractions 272/64,288/7409 is 16/474176

Least Common Multiple of 64,7409 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 64,7409 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(64,7409) = 1

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

GCF(64,7409) x common factors =1 x 1 = 1

LCM(64,7409) = ( 64 × 7409 ) / 1

LCM(64,7409) = 474176 / 1

LCM(64,7409) = 474176

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FAQs on GCF of Fractions of 272/64, 288/7409

1. What is the HCF of 272,288?

The HCF of 272,288 is 16

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 272/64, 288/7409?

Answer: GCF of Numerators as per given numbers 272/64, 288/7409 is

GCF of Numerators i.e. for 272,288 is 16

LCM of denominators i.e. for 64,7409 is 474176.

Thus, GCF of Fractions is 16/474176.Finally, GCF of Fractions for 272/64, 288/7409 is 16/474176.