Use our free GCF of Fractions Calculator tool to compute the GCF of 232/195, 828/156 i.e 4/780 easily. The following is the detailed procedure to determine the greatest common factor of fractions 232/195, 828/156.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 232/195,828/156
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 232/195,828/156, numerators are 232,828
Denominators are 195,156
The GCF of 232,828 is 4 .
LCM of 195,156 is 780.
The greatest common factor of 232/195,828/156 = [GCF of 232,828]/[LCM of 195,156]= 4/780
Therefore, the GCF of 232/195,828/156 is 4/780.
To find the highest common factor of 232,828, we have to find the factors of both numbers and list the highest common factor.
The factors of 232 are 1, 2, 4, 8, 29, 58, 116, 232
The factors of 828 are 1, 2, 3, 4, 6, 9, 12, 18, 23, 36, 46, 69, 92, 138, 207, 276, 414, 828
The HCF of 232,828 is 4.
Lets's calculate GCF of 232,828
2 | 232, 828 |
2 | 116, 414 |
58, 207 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Now, list down the factors of 232
:1,2,4,8,29,58,116,232
Now, list down the factors of 828
:1,2,3,4,6,9,12,18,23,36,46,69,92,138,207,276,414,828
Greatest Common Factor
We found the factors 232,828 . The biggest common factor number is the GCF number.
So the greatest common factor 232,828 is 4.
Lets's calculate LCM of 195,156
3 | 195, 156 |
13 | 65, 52 |
5, 4 |
∴ So the LCM of the given numbers is 3 x 13 x 5 x 4 = 780
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/780
Therefore, the GCF of Fractions 232/195,828/156 is 4/780
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 195,156 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(195,156) = 39
common factors(in case of two or more numbers have common factors) = 1
GCF(195,156) x common factors =39 x 1 = 39
LCM(195,156) = ( 195 × 156 ) / 39
LCM(195,156) = 30420 / 39
LCM(195,156) = 780
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 232,828?
The HCF of 232,828 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 232/195, 828/156?
Answer: GCF of Numerators as per given numbers 232/195, 828/156 is
GCF of Numerators i.e. for 232,828 is 4
LCM of denominators i.e. for 195,156 is 780.
Thus, GCF of Fractions is 4/780.Finally, GCF of Fractions for 232/195, 828/156 is 4/780.