Use our free GCF of Fractions Calculator tool to compute the GCF of 14/752, 17/384, 286/396 i.e 1/595584 easily. The following is the detailed procedure to determine the greatest common factor of fractions 14/752, 17/384, 286/396.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 14/752,17/384,286/396
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 14/752,17/384,286/396, numerators are 14,17,286
Denominators are 752,384,396
The GCF of 14,17,286 is 1 .
LCM of 752,384,396 is 595584.
The greatest common factor of 14/752,17/384,286/396 = [GCF of 14,17,286]/[LCM of 752,384,396]= 1/595584
Therefore, the GCF of 14/752,17/384,286/396 is 1/595584.
To find the highest common factor of 14,17,286, 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 17 are 1, 17
The factors of 286 are 1, 2, 11, 13, 22, 26, 143, 286
The HCF of 14,17,286 is 1.
Lets's calculate GCF of 14,17,286
∴ 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 17
:1,17
Now, list down the factors of 286
:1,2,11,13,22,26,143,286
Greatest Common Factor
We found the factors 14,17,286 . The biggest common factor number is the GCF number.
So the greatest common factor 14,17,286 is 1.
Lets's calculate LCM of 752,384,396
2 | 752, 384, 396 |
2 | 376, 192, 198 |
2 | 188, 96, 99 |
2 | 94, 48, 99 |
3 | 47, 24, 99 |
47, 8, 33 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 3 x 47 x 8 x 33 = 595584
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/595584
Therefore, the GCF of Fractions 14/752,17/384,286/396 is 1/595584
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 752,384,396 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(752,384,396) = 4
common factors(in case of two or more numbers have common factors) = 48
GCF(752,384,396) x common factors =4 x 48 = 192
LCM(752,384,396) = ( 752 × 384 × 396 ) / 192
LCM(752,384,396) = 114352128 / 192
LCM(752,384,396) = 595584
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 14,17,286?
The HCF of 14,17,286 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 14/752, 17/384, 286/396?
Answer: GCF of Numerators as per given numbers 14/752, 17/384, 286/396 is
GCF of Numerators i.e. for 14,17,286 is 1
LCM of denominators i.e. for 752,384,396 is 595584.
Thus, GCF of Fractions is 1/595584.Finally, GCF of Fractions for 14/752, 17/384, 286/396 is 1/595584.