Use our free GCF of Fractions Calculator tool to compute the GCF of 260/454, 280/202 i.e 20/45854 easily. The following is the detailed procedure to determine the greatest common factor of fractions 260/454, 280/202.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 260/454,280/202
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 260/454,280/202, numerators are 260,280
Denominators are 454,202
The GCF of 260,280 is 20 .
LCM of 454,202 is 45854.
The greatest common factor of 260/454,280/202 = [GCF of 260,280]/[LCM of 454,202]= 20/45854
Therefore, the GCF of 260/454,280/202 is 20/45854.
To find the highest common factor of 260,280, we have to find the factors of both numbers and list the highest common factor.
The factors of 260 are 1, 2, 4, 5, 10, 13, 20, 26, 52, 65, 130, 260
The factors of 280 are 1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 56, 70, 140, 280
The HCF of 260,280 is 20.
Lets's calculate GCF of 260,280
2 | 260, 280 |
2 | 130, 140 |
5 | 65, 70 |
13, 14 |
∴ So the GCF of the given numbers is 2 x 2 x 5 = 20
Now, list down the factors of 260
:1,2,4,5,10,13,20,26,52,65,130,260
Now, list down the factors of 280
:1,2,4,5,7,8,10,14,20,28,35,40,56,70,140,280
Greatest Common Factor
We found the factors 260,280 . The biggest common factor number is the GCF number.
So the greatest common factor 260,280 is 20.
Lets's calculate LCM of 454,202
2 | 454, 202 |
227, 101 |
∴ So the LCM of the given numbers is 2 x 227 x 101 = 45854
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 20/45854
Therefore, the GCF of Fractions 260/454,280/202 is 20/45854
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 454,202 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(454,202) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(454,202) x common factors =2 x 1 = 2
LCM(454,202) = ( 454 × 202 ) / 2
LCM(454,202) = 91708 / 2
LCM(454,202) = 45854
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 260,280?
The HCF of 260,280 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 260/454, 280/202?
Answer: GCF of Numerators as per given numbers 260/454, 280/202 is
GCF of Numerators i.e. for 260,280 is 20
LCM of denominators i.e. for 454,202 is 45854.
Thus, GCF of Fractions is 20/45854.Finally, GCF of Fractions for 260/454, 280/202 is 20/45854.