Use our free GCF of Fractions Calculator tool to compute the GCF of 448/242, 560/564 i.e 112/68244 easily. The following is the detailed procedure to determine the greatest common factor of fractions 448/242, 560/564.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 448/242,560/564
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 448/242,560/564, numerators are 448,560
Denominators are 242,564
The GCF of 448,560 is 112 .
LCM of 242,564 is 68244.
The greatest common factor of 448/242,560/564 = [GCF of 448,560]/[LCM of 242,564]= 112/68244
Therefore, the GCF of 448/242,560/564 is 112/68244.
To find the highest common factor of 448,560, 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 560 are 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 35, 40, 56, 70, 80, 112, 140, 280, 560
The HCF of 448,560 is 112.
Lets's calculate GCF of 448,560
2 | 448, 560 |
2 | 224, 280 |
2 | 112, 140 |
2 | 56, 70 |
7 | 28, 35 |
4, 5 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 x 7 = 112
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 560
:1,2,4,5,7,8,10,14,16,20,28,35,40,56,70,80,112,140,280,560
Greatest Common Factor
We found the factors 448,560 . The biggest common factor number is the GCF number.
So the greatest common factor 448,560 is 112.
Lets's calculate LCM of 242,564
2 | 242, 564 |
121, 282 |
∴ So the LCM of the given numbers is 2 x 121 x 282 = 68244
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 112/68244
Therefore, the GCF of Fractions 448/242,560/564 is 112/68244
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 242,564 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(242,564) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(242,564) x common factors =2 x 1 = 2
LCM(242,564) = ( 242 × 564 ) / 2
LCM(242,564) = 136488 / 2
LCM(242,564) = 68244
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 448,560?
The HCF of 448,560 is 112
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 448/242, 560/564?
Answer: GCF of Numerators as per given numbers 448/242, 560/564 is
GCF of Numerators i.e. for 448,560 is 112
LCM of denominators i.e. for 242,564 is 68244.
Thus, GCF of Fractions is 112/68244.Finally, GCF of Fractions for 448/242, 560/564 is 112/68244.