Use our free GCF of Fractions Calculator tool to compute the GCF of 480/570, 2140/736 i.e 20/209760 easily. The following is the detailed procedure to determine the greatest common factor of fractions 480/570, 2140/736.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 480/570,2140/736
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 480/570,2140/736, numerators are 480,2140
Denominators are 570,736
The GCF of 480,2140 is 20 .
LCM of 570,736 is 209760.
The greatest common factor of 480/570,2140/736 = [GCF of 480,2140]/[LCM of 570,736]= 20/209760
Therefore, the GCF of 480/570,2140/736 is 20/209760.
To find the highest common factor of 480,2140, we have to find the factors of both numbers and list the highest common factor.
The factors of 480 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 80, 96, 120, 160, 240, 480
The factors of 2140 are 1, 2, 4, 5, 10, 20, 107, 214, 428, 535, 1070, 2140
The HCF of 480,2140 is 20.
Lets's calculate GCF of 480,2140
2 | 480, 2140 |
2 | 240, 1070 |
5 | 120, 535 |
24, 107 |
∴ So the GCF of the given numbers is 2 x 2 x 5 = 20
Now, list down the factors of 480
:1,2,3,4,5,6,8,10,12,15,16,20,24,30,32,40,48,60,80,96,120,160,240,480
Now, list down the factors of 2140
:1,2,4,5,10,20,107,214,428,535,1070,2140
Greatest Common Factor
We found the factors 480,2140 . The biggest common factor number is the GCF number.
So the greatest common factor 480,2140 is 20.
Lets's calculate LCM of 570,736
2 | 570, 736 |
285, 368 |
∴ So the LCM of the given numbers is 2 x 285 x 368 = 209760
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 20/209760
Therefore, the GCF of Fractions 480/570,2140/736 is 20/209760
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 570,736 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(570,736) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(570,736) x common factors =2 x 1 = 2
LCM(570,736) = ( 570 × 736 ) / 2
LCM(570,736) = 419520 / 2
LCM(570,736) = 209760
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 480,2140?
The HCF of 480,2140 is 20
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 480/570, 2140/736?
Answer: GCF of Numerators as per given numbers 480/570, 2140/736 is
GCF of Numerators i.e. for 480,2140 is 20
LCM of denominators i.e. for 570,736 is 209760.
Thus, GCF of Fractions is 20/209760.Finally, GCF of Fractions for 480/570, 2140/736 is 20/209760.