GCF of 448/821, 512/344
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 448/821, 512/344 i.e 64/282424 easily. The following is the detailed procedure to determine the greatest common factor of fractions 448/821, 512/344.
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 448/821,512/344?
Given fractions are 448/821,512/344
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 448/821,512/344, numerators are 448,512
Denominators are 821,344
The GCF of 448,512 is 64 .
LCM of 821,344 is 282424.
The greatest common factor of 448/821,512/344 = [GCF of 448,512]/[LCM of 821,344]= 64/282424
Therefore, the GCF of 448/821,512/344 is 64/282424.
To find the highest common factor of 448,512, 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 512 are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512
The HCF of 448,512 is 64.
Lets's calculate GCF of 448,512
| 2 | 448, 512 |
| 2 | 224, 256 |
| 2 | 112, 128 |
| 2 | 56, 64 |
| 2 | 28, 32 |
| 2 | 14, 16 |
| 7, 8 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 x 2 x 2 = 64
Greatest Common Factor of 448,512 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 512
:1,2,4,8,16,32,64,128,256,512
Greatest Common Factor
We found the factors 448,512 . The biggest common factor number is the GCF number.
So the greatest common factor 448,512 is 64.
Lets's calculate LCM of 821,344
Given numbers has no common factors except 1. So, there LCM is their product i.e 282424
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 64/282424
Therefore, the GCF of Fractions 448/821,512/344 is 64/282424
Least Common Multiple of 821,344 with GCF Formula
The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).
We need to calculate greatest common factor of 821,344 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(821,344) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(821,344) x common factors =1 x 1 = 1
LCM(821,344) = ( 821 × 344 ) / 1
LCM(821,344) = 282424 / 1
LCM(821,344) = 282424
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FAQs on GCF of Fractions of 448/821, 512/344
1. What is the HCF of 448,512?
The HCF of 448,512 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 448/821, 512/344?
Answer: GCF of Numerators as per given numbers 448/821, 512/344 is
GCF of Numerators i.e. for 448,512 is 64
LCM of denominators i.e. for 821,344 is 282424.
Thus, GCF of Fractions is 64/282424.Finally, GCF of Fractions for 448/821, 512/344 is 64/282424.