Use our free GCF of Fractions Calculator tool to compute the GCF of 728/68, 208/305 i.e 104/20740 easily. The following is the detailed procedure to determine the greatest common factor of fractions 728/68, 208/305.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 728/68,208/305
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 728/68,208/305, numerators are 728,208
Denominators are 68,305
The GCF of 728,208 is 104 .
LCM of 68,305 is 20740.
The greatest common factor of 728/68,208/305 = [GCF of 728,208]/[LCM of 68,305]= 104/20740
Therefore, the GCF of 728/68,208/305 is 104/20740.
To find the highest common factor of 728,208, we have to find the factors of both numbers and list the highest common factor.
The factors of 728 are 1, 2, 4, 7, 8, 13, 14, 26, 28, 52, 56, 91, 104, 182, 364, 728
The factors of 208 are 1, 2, 4, 8, 13, 16, 26, 52, 104, 208
The HCF of 728,208 is 104.
Lets's calculate GCF of 728,208
2 | 728, 208 |
2 | 364, 104 |
2 | 182, 52 |
13 | 91, 26 |
7, 2 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 13 = 104
Now, list down the factors of 728
:1,2,4,7,8,13,14,26,28,52,56,91,104,182,364,728
Now, list down the factors of 208
:1,2,4,8,13,16,26,52,104,208
Greatest Common Factor
We found the factors 728,208 . The biggest common factor number is the GCF number.
So the greatest common factor 728,208 is 104.
Lets's calculate LCM of 68,305
Given numbers has no common factors except 1. So, there LCM is their product i.e 20740
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 104/20740
Therefore, the GCF of Fractions 728/68,208/305 is 104/20740
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 68,305 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(68,305) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(68,305) x common factors =1 x 1 = 1
LCM(68,305) = ( 68 × 305 ) / 1
LCM(68,305) = 20740 / 1
LCM(68,305) = 20740
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 728,208?
The HCF of 728,208 is 104
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 728/68, 208/305?
Answer: GCF of Numerators as per given numbers 728/68, 208/305 is
GCF of Numerators i.e. for 728,208 is 104
LCM of denominators i.e. for 68,305 is 20740.
Thus, GCF of Fractions is 104/20740.Finally, GCF of Fractions for 728/68, 208/305 is 104/20740.