Use our free GCF of Fractions Calculator tool to compute the GCF of 916/142, 296/728 i.e 4/51688 easily. The following is the detailed procedure to determine the greatest common factor of fractions 916/142, 296/728.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 916/142,296/728
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 916/142,296/728, numerators are 916,296
Denominators are 142,728
The GCF of 916,296 is 4 .
LCM of 142,728 is 51688.
The greatest common factor of 916/142,296/728 = [GCF of 916,296]/[LCM of 142,728]= 4/51688
Therefore, the GCF of 916/142,296/728 is 4/51688.
To find the highest common factor of 916,296, we have to find the factors of both numbers and list the highest common factor.
The factors of 916 are 1, 2, 4, 229, 458, 916
The factors of 296 are 1, 2, 4, 8, 37, 74, 148, 296
The HCF of 916,296 is 4.
Lets's calculate GCF of 916,296
2 | 916, 296 |
2 | 458, 148 |
229, 74 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Now, list down the factors of 916
:1,2,4,229,458,916
Now, list down the factors of 296
:1,2,4,8,37,74,148,296
Greatest Common Factor
We found the factors 916,296 . The biggest common factor number is the GCF number.
So the greatest common factor 916,296 is 4.
Lets's calculate LCM of 142,728
2 | 142, 728 |
71, 364 |
∴ So the LCM of the given numbers is 2 x 71 x 364 = 51688
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/51688
Therefore, the GCF of Fractions 916/142,296/728 is 4/51688
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 142,728 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(142,728) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(142,728) x common factors =2 x 1 = 2
LCM(142,728) = ( 142 × 728 ) / 2
LCM(142,728) = 103376 / 2
LCM(142,728) = 51688
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 916,296?
The HCF of 916,296 is 4
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 916/142, 296/728?
Answer: GCF of Numerators as per given numbers 916/142, 296/728 is
GCF of Numerators i.e. for 916,296 is 4
LCM of denominators i.e. for 142,728 is 51688.
Thus, GCF of Fractions is 4/51688.Finally, GCF of Fractions for 916/142, 296/728 is 4/51688.