Use our free GCF of Fractions Calculator tool to compute the GCF of 430/802, 480/254 i.e 10/101854 easily. The following is the detailed procedure to determine the greatest common factor of fractions 430/802, 480/254.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 430/802,480/254
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 430/802,480/254, numerators are 430,480
Denominators are 802,254
The GCF of 430,480 is 10 .
LCM of 802,254 is 101854.
The greatest common factor of 430/802,480/254 = [GCF of 430,480]/[LCM of 802,254]= 10/101854
Therefore, the GCF of 430/802,480/254 is 10/101854.
To find the highest common factor of 430,480, we have to find the factors of both numbers and list the highest common factor.
The factors of 430 are 1, 2, 5, 10, 43, 86, 215, 430
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 HCF of 430,480 is 10.
Lets's calculate GCF of 430,480
2 | 430, 480 |
5 | 215, 240 |
43, 48 |
∴ So the GCF of the given numbers is 2 x 5 = 10
Now, list down the factors of 430
:1,2,5,10,43,86,215,430
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
Greatest Common Factor
We found the factors 430,480 . The biggest common factor number is the GCF number.
So the greatest common factor 430,480 is 10.
Lets's calculate LCM of 802,254
2 | 802, 254 |
401, 127 |
∴ So the LCM of the given numbers is 2 x 401 x 127 = 101854
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/101854
Therefore, the GCF of Fractions 430/802,480/254 is 10/101854
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 802,254 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(802,254) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(802,254) x common factors =2 x 1 = 2
LCM(802,254) = ( 802 × 254 ) / 2
LCM(802,254) = 203708 / 2
LCM(802,254) = 101854
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 430,480?
The HCF of 430,480 is 10
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 430/802, 480/254?
Answer: GCF of Numerators as per given numbers 430/802, 480/254 is
GCF of Numerators i.e. for 430,480 is 10
LCM of denominators i.e. for 802,254 is 101854.
Thus, GCF of Fractions is 10/101854.Finally, GCF of Fractions for 430/802, 480/254 is 10/101854.