Use our free GCF of Fractions Calculator tool to compute the GCF of 14/19, 16/262, 782/200 i.e 2/497800 easily. The following is the detailed procedure to determine the greatest common factor of fractions 14/19, 16/262, 782/200.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 14/19,16/262,782/200
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 14/19,16/262,782/200, numerators are 14,16,782
Denominators are 19,262,200
The GCF of 14,16,782 is 2 .
LCM of 19,262,200 is 497800.
The greatest common factor of 14/19,16/262,782/200 = [GCF of 14,16,782]/[LCM of 19,262,200]= 2/497800
Therefore, the GCF of 14/19,16/262,782/200 is 2/497800.
To find the highest common factor of 14,16,782, 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 16 are 1, 2, 4, 8, 16
The factors of 782 are 1, 2, 17, 23, 34, 46, 391, 782
The HCF of 14,16,782 is 2.
Lets's calculate GCF of 14,16,782
2 | 14, 16, 782 |
7, 8, 391 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 14
:1,2,7,14
Now, list down the factors of 16
:1,2,4,8,16
Now, list down the factors of 782
:1,2,17,23,34,46,391,782
Greatest Common Factor
We found the factors 14,16,782 . The biggest common factor number is the GCF number.
So the greatest common factor 14,16,782 is 2.
Lets's calculate LCM of 19,262,200
2 | 19, 262, 200 |
19, 131, 100 |
∴ So the LCM of the given numbers is 2 x 19 x 131 x 100 = 497800
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/497800
Therefore, the GCF of Fractions 14/19,16/262,782/200 is 2/497800
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 19,262,200 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(19,262,200) = 1
common factors(in case of two or more numbers have common factors) = 2
GCF(19,262,200) x common factors =1 x 2 = 2
LCM(19,262,200) = ( 19 × 262 × 200 ) / 2
LCM(19,262,200) = 995600 / 2
LCM(19,262,200) = 497800
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 14,16,782?
The HCF of 14,16,782 is 2
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 14/19, 16/262, 782/200?
Answer: GCF of Numerators as per given numbers 14/19, 16/262, 782/200 is
GCF of Numerators i.e. for 14,16,782 is 2
LCM of denominators i.e. for 19,262,200 is 497800.
Thus, GCF of Fractions is 2/497800.Finally, GCF of Fractions for 14/19, 16/262, 782/200 is 2/497800.