How to Find GCF of 448/875, 640/514?

GCF of 448/875, 640/514

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 448/875, 640/514 i.e 64/449750 easily. The following is the detailed procedure to determine the greatest common factor of fractions 448/875, 640/514.

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 448/875,640/514?

Given fractions are 448/875,640/514

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 448/875,640/514, numerators are 448,640

Denominators are 875,514

The GCF of 448,640 is 64 .

LCM of 875,514 is 449750.

The greatest common factor of 448/875,640/514 = [GCF of 448,640]/[LCM of 875,514]= 64/449750

Therefore, the GCF of 448/875,640/514 is 64/449750.

Greatest Common Factor of 448,640

To find the highest common factor of 448,640, we have to find the factors of both numbers and list the highest common factor.

The factors of 448 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 224, 448

The factors of 640 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 128, 160, 320, 640

The HCF of 448,640 is 64.

Lets's calculate GCF of 448,640

Greatest Common Factor (GCF) of 448,640 By Common Division

2	448, 640
2	224, 320
2	112, 160
2	56, 80
2	28, 40
2	14, 20
	7, 10

∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 x 2 x 2 = 64

Greatest Common Factor of 448,640 By Matching Biggest Common Factor Method

Now, list down the factors of 448

1,2,4,7,8,14,16,28,32,56,64,112,224,448

Now, list down the factors of 640

1,2,4,5,8,10,16,20,32,40,64,80,128,160,320,640

Greatest Common Factor

We found the factors 448,640 . The biggest common factor number is the GCF number.
So the greatest common factor 448,640 is 64.

Lets's calculate LCM of 875,514

Lowest Common Multiple of 875,514 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 449750

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 64/449750

Therefore, the GCF of Fractions 448/875,640/514 is 64/449750

Least Common Multiple of 875,514 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 875,514 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(875,514) = 1

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

GCF(875,514) x common factors =1 x 1 = 1

LCM(875,514) = ( 875 × 514 ) / 1

LCM(875,514) = 449750 / 1

LCM(875,514) = 449750

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FAQs on GCF of Fractions of 448/875, 640/514

1. What is the HCF of 448,640?

The HCF of 448,640 is 64

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 448/875, 640/514?

Answer: GCF of Numerators as per given numbers 448/875, 640/514 is

GCF of Numerators i.e. for 448,640 is 64

LCM of denominators i.e. for 875,514 is 449750.

Thus, GCF of Fractions is 64/449750.Finally, GCF of Fractions for 448/875, 640/514 is 64/449750.