Use our free GCF of Fractions Calculator tool to compute the GCF of 448/462, 2114/8744 i.e 14/2019864 easily. The following is the detailed procedure to determine the greatest common factor of fractions 448/462, 2114/8744.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 448/462,2114/8744
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 448/462,2114/8744, numerators are 448,2114
Denominators are 462,8744
The GCF of 448,2114 is 14 .
LCM of 462,8744 is 2019864.
The greatest common factor of 448/462,2114/8744 = [GCF of 448,2114]/[LCM of 462,8744]= 14/2019864
Therefore, the GCF of 448/462,2114/8744 is 14/2019864.
To find the highest common factor of 448,2114, 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 2114 are 1, 2, 7, 14, 151, 302, 1057, 2114
The HCF of 448,2114 is 14.
Lets's calculate GCF of 448,2114
2 | 448, 2114 |
7 | 224, 1057 |
32, 151 |
∴ So the GCF of the given numbers is 2 x 7 = 14
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 2114
:1,2,7,14,151,302,1057,2114
Greatest Common Factor
We found the factors 448,2114 . The biggest common factor number is the GCF number.
So the greatest common factor 448,2114 is 14.
Lets's calculate LCM of 462,8744
2 | 462, 8744 |
231, 4372 |
∴ So the LCM of the given numbers is 2 x 231 x 4372 = 2019864
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/2019864
Therefore, the GCF of Fractions 448/462,2114/8744 is 14/2019864
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 462,8744 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(462,8744) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(462,8744) x common factors =2 x 1 = 2
LCM(462,8744) = ( 462 × 8744 ) / 2
LCM(462,8744) = 4039728 / 2
LCM(462,8744) = 2019864
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 448,2114?
The HCF of 448,2114 is 14
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 448/462, 2114/8744?
Answer: GCF of Numerators as per given numbers 448/462, 2114/8744 is
GCF of Numerators i.e. for 448,2114 is 14
LCM of denominators i.e. for 462,8744 is 2019864.
Thus, GCF of Fractions is 14/2019864.Finally, GCF of Fractions for 448/462, 2114/8744 is 14/2019864.