Use our free GCF of Fractions Calculator tool to compute the GCF of 312/103, 728/821 i.e 104/84563 easily. The following is the detailed procedure to determine the greatest common factor of fractions 312/103, 728/821.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 312/103,728/821
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 312/103,728/821, numerators are 312,728
Denominators are 103,821
The GCF of 312,728 is 104 .
LCM of 103,821 is 84563.
The greatest common factor of 312/103,728/821 = [GCF of 312,728]/[LCM of 103,821]= 104/84563
Therefore, the GCF of 312/103,728/821 is 104/84563.
To find the highest common factor of 312,728, we have to find the factors of both numbers and list the highest common factor.
The factors of 312 are 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312
The factors of 728 are 1, 2, 4, 7, 8, 13, 14, 26, 28, 52, 56, 91, 104, 182, 364, 728
The HCF of 312,728 is 104.
Lets's calculate GCF of 312,728
2 | 312, 728 |
2 | 156, 364 |
2 | 78, 182 |
13 | 39, 91 |
3, 7 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 13 = 104
Now, list down the factors of 312
:1,2,3,4,6,8,12,13,24,26,39,52,78,104,156,312
Now, list down the factors of 728
:1,2,4,7,8,13,14,26,28,52,56,91,104,182,364,728
Greatest Common Factor
We found the factors 312,728 . The biggest common factor number is the GCF number.
So the greatest common factor 312,728 is 104.
Lets's calculate LCM of 103,821
Given numbers has no common factors except 1. So, there LCM is their product i.e 84563
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 104/84563
Therefore, the GCF of Fractions 312/103,728/821 is 104/84563
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 103,821 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(103,821) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(103,821) x common factors =1 x 1 = 1
LCM(103,821) = ( 103 × 821 ) / 1
LCM(103,821) = 84563 / 1
LCM(103,821) = 84563
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 312,728?
The HCF of 312,728 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 312/103, 728/821?
Answer: GCF of Numerators as per given numbers 312/103, 728/821 is
GCF of Numerators i.e. for 312,728 is 104
LCM of denominators i.e. for 103,821 is 84563.
Thus, GCF of Fractions is 104/84563.Finally, GCF of Fractions for 312/103, 728/821 is 104/84563.