Use our free GCF of Fractions Calculator tool to compute the GCF of 65/900, 25/5104 i.e 5/1148400 easily. The following is the detailed procedure to determine the greatest common factor of fractions 65/900, 25/5104.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 65/900,25/5104
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 65/900,25/5104, numerators are 65,25
Denominators are 900,5104
The GCF of 65,25 is 5 .
LCM of 900,5104 is 1148400.
The greatest common factor of 65/900,25/5104 = [GCF of 65,25]/[LCM of 900,5104]= 5/1148400
Therefore, the GCF of 65/900,25/5104 is 5/1148400.
To find the highest common factor of 65,25, we have to find the factors of both numbers and list the highest common factor.
The factors of 65 are 1, 5, 13, 65
The factors of 25 are 1, 5, 25
The HCF of 65,25 is 5.
Lets's calculate GCF of 65,25
5 | 65, 25 |
13, 5 |
∴ So the GCF of the given numbers is 5 = 5
Lets's calculate LCM of 900,5104
2 | 900, 5104 |
2 | 450, 2552 |
225, 1276 |
∴ So the LCM of the given numbers is 2 x 2 x 225 x 1276 = 1148400
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/1148400
Therefore, the GCF of Fractions 65/900,25/5104 is 5/1148400
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 900,5104 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(900,5104) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(900,5104) x common factors =4 x 1 = 4
LCM(900,5104) = ( 900 × 5104 ) / 4
LCM(900,5104) = 4593600 / 4
LCM(900,5104) = 1148400
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 65,25?
The HCF of 65,25 is 5
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 65/900, 25/5104?
Answer: GCF of Numerators as per given numbers 65/900, 25/5104 is
GCF of Numerators i.e. for 65,25 is 5
LCM of denominators i.e. for 900,5104 is 1148400.
Thus, GCF of Fractions is 5/1148400.Finally, GCF of Fractions for 65/900, 25/5104 is 5/1148400.