Use our free GCF of Fractions Calculator tool to compute the GCF of 14/75, 100/86, 803/516 i.e 1/12900 easily. The following is the detailed procedure to determine the greatest common factor of fractions 14/75, 100/86, 803/516.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 14/75,100/86,803/516
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 14/75,100/86,803/516, numerators are 14,100,803
Denominators are 75,86,516
The GCF of 14,100,803 is 1 .
LCM of 75,86,516 is 12900.
The greatest common factor of 14/75,100/86,803/516 = [GCF of 14,100,803]/[LCM of 75,86,516]= 1/12900
Therefore, the GCF of 14/75,100/86,803/516 is 1/12900.
To find the highest common factor of 14,100,803, we have to find the factors of both numbers and list the highest common factor.
The factors of 14 are 1, 2, 7, 14
The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, 100
The factors of 803 are 1, 11, 73, 803
The HCF of 14,100,803 is 1.
Lets's calculate GCF of 14,100,803
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 14
:1,2,7,14
Now, list down the factors of 100
:1,2,4,5,10,20,25,50,100
Now, list down the factors of 803
:1,11,73,803
Greatest Common Factor
We found the factors 14,100,803 . The biggest common factor number is the GCF number.
So the greatest common factor 14,100,803 is 1.
Lets's calculate LCM of 75,86,516
2 | 75, 86, 516 |
3 | 75, 43, 258 |
43 | 25, 43, 86 |
25, 1, 2 |
∴ So the LCM of the given numbers is 2 x 3 x 43 x 25 x 1 x 2 = 12900
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/12900
Therefore, the GCF of Fractions 14/75,100/86,803/516 is 1/12900
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 75,86,516 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(75,86,516) = 1
common factors(in case of two or more numbers have common factors) = 258
GCF(75,86,516) x common factors =1 x 258 = 258
LCM(75,86,516) = ( 75 × 86 × 516 ) / 258
LCM(75,86,516) = 3328200 / 258
LCM(75,86,516) = 12900
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 14,100,803?
The HCF of 14,100,803 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 14/75, 100/86, 803/516?
Answer: GCF of Numerators as per given numbers 14/75, 100/86, 803/516 is
GCF of Numerators i.e. for 14,100,803 is 1
LCM of denominators i.e. for 75,86,516 is 12900.
Thus, GCF of Fractions is 1/12900.Finally, GCF of Fractions for 14/75, 100/86, 803/516 is 1/12900.