Use our free GCF of Fractions Calculator tool to compute the GCF of 464/550, 140/305 i.e 4/33550 easily. The following is the detailed procedure to determine the greatest common factor of fractions 464/550, 140/305.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 464/550,140/305
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 464/550,140/305, numerators are 464,140
Denominators are 550,305
The GCF of 464,140 is 4 .
LCM of 550,305 is 33550.
The greatest common factor of 464/550,140/305 = [GCF of 464,140]/[LCM of 550,305]= 4/33550
Therefore, the GCF of 464/550,140/305 is 4/33550.
To find the highest common factor of 464,140, we have to find the factors of both numbers and list the highest common factor.
The factors of 464 are 1, 2, 4, 8, 16, 29, 58, 116, 232, 464
The factors of 140 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140
The HCF of 464,140 is 4.
Lets's calculate GCF of 464,140
2 | 464, 140 |
2 | 232, 70 |
116, 35 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Now, list down the factors of 464
:1,2,4,8,16,29,58,116,232,464
Now, list down the factors of 140
:1,2,4,5,7,10,14,20,28,35,70,140
Greatest Common Factor
We found the factors 464,140 . The biggest common factor number is the GCF number.
So the greatest common factor 464,140 is 4.
Lets's calculate LCM of 550,305
5 | 550, 305 |
110, 61 |
∴ So the LCM of the given numbers is 5 x 110 x 61 = 33550
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/33550
Therefore, the GCF of Fractions 464/550,140/305 is 4/33550
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 550,305 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(550,305) = 5
common factors(in case of two or more numbers have common factors) = 1
GCF(550,305) x common factors =5 x 1 = 5
LCM(550,305) = ( 550 × 305 ) / 5
LCM(550,305) = 167750 / 5
LCM(550,305) = 33550
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 464,140?
The HCF of 464,140 is 4
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 464/550, 140/305?
Answer: GCF of Numerators as per given numbers 464/550, 140/305 is
GCF of Numerators i.e. for 464,140 is 4
LCM of denominators i.e. for 550,305 is 33550.
Thus, GCF of Fractions is 4/33550.Finally, GCF of Fractions for 464/550, 140/305 is 4/33550.