How to Find GCF of 754/136, 728/336?

GCF of 754/136, 728/336

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 754/136, 728/336 i.e 26/5712 easily. The following is the detailed procedure to determine the greatest common factor of fractions 754/136, 728/336.

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 754/136,728/336?

Given fractions are 754/136,728/336

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 754/136,728/336, numerators are 754,728

Denominators are 136,336

The GCF of 754,728 is 26 .

LCM of 136,336 is 5712.

The greatest common factor of 754/136,728/336 = [GCF of 754,728]/[LCM of 136,336]= 26/5712

Therefore, the GCF of 754/136,728/336 is 26/5712.

Greatest Common Factor of 754,728

To find the highest common factor of 754,728, we have to find the factors of both numbers and list the highest common factor.

The factors of 754 are 1, 2, 13, 26, 29, 58, 377, 754

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

The HCF of 754,728 is 26.

Lets's calculate GCF of 754,728

Greatest Common Factor (GCF) of 754,728 By Common Division

2	754, 728
13	377, 364
	29, 28

∴ So the GCF of the given numbers is 2 x 13 = 26

Greatest Common Factor of 754,728 By Matching Biggest Common Factor Method

Now, list down the factors of 754

1,2,13,26,29,58,377,754

Now, list down the factors of 728

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

Greatest Common Factor

We found the factors 754,728 . The biggest common factor number is the GCF number.
So the greatest common factor 754,728 is 26.

Lets's calculate LCM of 136,336

Lowest Common Multiple of 136,336 using Common Division

2	136, 336
2	68, 168
2	34, 84
	17, 42

∴ So the LCM of the given numbers is 2 x 2 x 2 x 17 x 42 = 5712

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 26/5712

Therefore, the GCF of Fractions 754/136,728/336 is 26/5712

Least Common Multiple of 136,336 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 136,336 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(136,336) = 8

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

GCF(136,336) x common factors =8 x 1 = 8

LCM(136,336) = ( 136 × 336 ) / 8

LCM(136,336) = 45696 / 8

LCM(136,336) = 5712

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 754/136, 728/336

1. What is the HCF of 754,728?

The HCF of 754,728 is 26

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 754/136, 728/336?

Answer: GCF of Numerators as per given numbers 754/136, 728/336 is

GCF of Numerators i.e. for 754,728 is 26

LCM of denominators i.e. for 136,336 is 5712.

Thus, GCF of Fractions is 26/5712.Finally, GCF of Fractions for 754/136, 728/336 is 26/5712.