How to Find GCF of 728/237, 288/119?

GCF of 728/237, 288/119

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 728/237, 288/119 i.e 8/28203 easily. The following is the detailed procedure to determine the greatest common factor of fractions 728/237, 288/119.

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 728/237,288/119?

Given fractions are 728/237,288/119

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 728/237,288/119, numerators are 728,288

Denominators are 237,119

The GCF of 728,288 is 8 .

LCM of 237,119 is 28203.

The greatest common factor of 728/237,288/119 = [GCF of 728,288]/[LCM of 237,119]= 8/28203

Therefore, the GCF of 728/237,288/119 is 8/28203.

Greatest Common Factor of 728,288

To find the highest common factor of 728,288, we have to find the factors of both numbers and list the highest common factor.

The factors of 728 are 1, 2, 4, 7, 8, 13, 14, 26, 28, 52, 56, 91, 104, 182, 364, 728

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 728,288 is 8.

Lets's calculate GCF of 728,288

Greatest Common Factor (GCF) of 728,288 By Common Division

2	728, 288
2	364, 144
2	182, 72
	91, 36

∴ So the GCF of the given numbers is 2 x 2 x 2 = 8

Greatest Common Factor of 728,288 By Matching Biggest Common Factor Method

Now, list down the factors of 728

1,2,4,7,8,13,14,26,28,52,56,91,104,182,364,728

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 728,288 . The biggest common factor number is the GCF number.
So the greatest common factor 728,288 is 8.

Lets's calculate LCM of 237,119

Lowest Common Multiple of 237,119 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 28203

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 8/28203

Therefore, the GCF of Fractions 728/237,288/119 is 8/28203

Least Common Multiple of 237,119 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 237,119 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(237,119) = 1

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

GCF(237,119) x common factors =1 x 1 = 1

LCM(237,119) = ( 237 × 119 ) / 1

LCM(237,119) = 28203 / 1

LCM(237,119) = 28203

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FAQs on GCF of Fractions of 728/237, 288/119

1. What is the HCF of 728,288?

The HCF of 728,288 is 8

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 728/237, 288/119?

Answer: GCF of Numerators as per given numbers 728/237, 288/119 is

GCF of Numerators i.e. for 728,288 is 8

LCM of denominators i.e. for 237,119 is 28203.

Thus, GCF of Fractions is 8/28203.Finally, GCF of Fractions for 728/237, 288/119 is 8/28203.