Use our free GCF of Fractions Calculator tool to compute the GCF of 322/720, 904/560 i.e 2/5040 easily. The following is the detailed procedure to determine the greatest common factor of fractions 322/720, 904/560.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 322/720,904/560
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 322/720,904/560, numerators are 322,904
Denominators are 720,560
The GCF of 322,904 is 2 .
LCM of 720,560 is 5040.
The greatest common factor of 322/720,904/560 = [GCF of 322,904]/[LCM of 720,560]= 2/5040
Therefore, the GCF of 322/720,904/560 is 2/5040.
To find the highest common factor of 322,904, we have to find the factors of both numbers and list the highest common factor.
The factors of 322 are 1, 2, 7, 14, 23, 46, 161, 322
The factors of 904 are 1, 2, 4, 8, 113, 226, 452, 904
The HCF of 322,904 is 2.
Lets's calculate GCF of 322,904
2 | 322, 904 |
161, 452 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 322
:1,2,7,14,23,46,161,322
Now, list down the factors of 904
:1,2,4,8,113,226,452,904
Greatest Common Factor
We found the factors 322,904 . The biggest common factor number is the GCF number.
So the greatest common factor 322,904 is 2.
Lets's calculate LCM of 720,560
2 | 720, 560 |
2 | 360, 280 |
2 | 180, 140 |
2 | 90, 70 |
5 | 45, 35 |
9, 7 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 5 x 9 x 7 = 5040
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/5040
Therefore, the GCF of Fractions 322/720,904/560 is 2/5040
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 720,560 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(720,560) = 80
common factors(in case of two or more numbers have common factors) = 1
GCF(720,560) x common factors =80 x 1 = 80
LCM(720,560) = ( 720 × 560 ) / 80
LCM(720,560) = 403200 / 80
LCM(720,560) = 5040
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 322,904?
The HCF of 322,904 is 2
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 322/720, 904/560?
Answer: GCF of Numerators as per given numbers 322/720, 904/560 is
GCF of Numerators i.e. for 322,904 is 2
LCM of denominators i.e. for 720,560 is 5040.
Thus, GCF of Fractions is 2/5040.Finally, GCF of Fractions for 322/720, 904/560 is 2/5040.