How to Find GCF of 752/52, 576/413?

GCF of 752/52, 576/413

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 752/52, 576/413 i.e 16/21476 easily. The following is the detailed procedure to determine the greatest common factor of fractions 752/52, 576/413.

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 752/52,576/413?

Given fractions are 752/52,576/413

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 752/52,576/413, numerators are 752,576

Denominators are 52,413

The GCF of 752,576 is 16 .

LCM of 52,413 is 21476.

The greatest common factor of 752/52,576/413 = [GCF of 752,576]/[LCM of 52,413]= 16/21476

Therefore, the GCF of 752/52,576/413 is 16/21476.

Greatest Common Factor of 752,576

To find the highest common factor of 752,576, we have to find the factors of both numbers and list the highest common factor.

The factors of 752 are 1, 2, 4, 8, 16, 47, 94, 188, 376, 752

The factors of 576 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 144, 192, 288, 576

The HCF of 752,576 is 16.

Lets's calculate GCF of 752,576

Greatest Common Factor (GCF) of 752,576 By Common Division

2	752, 576
2	376, 288
2	188, 144
2	94, 72
	47, 36

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

Greatest Common Factor of 752,576 By Matching Biggest Common Factor Method

Now, list down the factors of 752

1,2,4,8,16,47,94,188,376,752

Now, list down the factors of 576

1,2,3,4,6,8,9,12,16,18,24,32,36,48,64,72,96,144,192,288,576

Greatest Common Factor

We found the factors 752,576 . The biggest common factor number is the GCF number.
So the greatest common factor 752,576 is 16.

Lets's calculate LCM of 52,413

Lowest Common Multiple of 52,413 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 21476

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 16/21476

Therefore, the GCF of Fractions 752/52,576/413 is 16/21476

Least Common Multiple of 52,413 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 52,413 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(52,413) = 1

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

GCF(52,413) x common factors =1 x 1 = 1

LCM(52,413) = ( 52 × 413 ) / 1

LCM(52,413) = 21476 / 1

LCM(52,413) = 21476

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 752/52, 576/413

1. What is the HCF of 752,576?

The HCF of 752,576 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 752/52, 576/413?

Answer: GCF of Numerators as per given numbers 752/52, 576/413 is

GCF of Numerators i.e. for 752,576 is 16

LCM of denominators i.e. for 52,413 is 21476.

Thus, GCF of Fractions is 16/21476.Finally, GCF of Fractions for 752/52, 576/413 is 16/21476.