Use our free GCF of Fractions Calculator tool to compute the GCF of 13/40, 561/99, 117/384 i.e 1/63360 easily. The following is the detailed procedure to determine the greatest common factor of fractions 13/40, 561/99, 117/384.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 13/40,561/99,117/384
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 13/40,561/99,117/384, numerators are 13,561,117
Denominators are 40,99,384
The GCF of 13,561,117 is 1 .
LCM of 40,99,384 is 63360.
The greatest common factor of 13/40,561/99,117/384 = [GCF of 13,561,117]/[LCM of 40,99,384]= 1/63360
Therefore, the GCF of 13/40,561/99,117/384 is 1/63360.
To find the highest common factor of 13,561,117, we have to find the factors of both numbers and list the highest common factor.
The factors of 13 are 1, 13
The factors of 561 are 1, 3, 11, 17, 33, 51, 187, 561
The factors of 117 are 1, 3, 9, 13, 39, 117
The HCF of 13,561,117 is 1.
Lets's calculate GCF of 13,561,117
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 13
:1,13
Now, list down the factors of 561
:1,3,11,17,33,51,187,561
Now, list down the factors of 117
:1,3,9,13,39,117
Greatest Common Factor
We found the factors 13,561,117 . The biggest common factor number is the GCF number.
So the greatest common factor 13,561,117 is 1.
Lets's calculate LCM of 40,99,384
2 | 40, 99, 384 |
2 | 20, 99, 192 |
2 | 10, 99, 96 |
3 | 5, 99, 48 |
5, 33, 16 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 3 x 5 x 33 x 16 = 63360
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/63360
Therefore, the GCF of Fractions 13/40,561/99,117/384 is 1/63360
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 40,99,384 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(40,99,384) = 1
common factors(in case of two or more numbers have common factors) = 24
GCF(40,99,384) x common factors =1 x 24 = 24
LCM(40,99,384) = ( 40 × 99 × 384 ) / 24
LCM(40,99,384) = 1520640 / 24
LCM(40,99,384) = 63360
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 13,561,117?
The HCF of 13,561,117 is 1
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 13/40, 561/99, 117/384?
Answer: GCF of Numerators as per given numbers 13/40, 561/99, 117/384 is
GCF of Numerators i.e. for 13,561,117 is 1
LCM of denominators i.e. for 40,99,384 is 63360.
Thus, GCF of Fractions is 1/63360.Finally, GCF of Fractions for 13/40, 561/99, 117/384 is 1/63360.