Use our free GCF of Fractions Calculator tool to compute the GCF of 77/19, 580/72, 192/132 i.e 1/15048 easily. The following is the detailed procedure to determine the greatest common factor of fractions 77/19, 580/72, 192/132.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 77/19,580/72,192/132
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 77/19,580/72,192/132, numerators are 77,580,192
Denominators are 19,72,132
The GCF of 77,580,192 is 1 .
LCM of 19,72,132 is 15048.
The greatest common factor of 77/19,580/72,192/132 = [GCF of 77,580,192]/[LCM of 19,72,132]= 1/15048
Therefore, the GCF of 77/19,580/72,192/132 is 1/15048.
To find the highest common factor of 77,580,192, we have to find the factors of both numbers and list the highest common factor.
The factors of 77 are 1, 7, 11, 77
The factors of 580 are 1, 2, 4, 5, 10, 20, 29, 58, 116, 145, 290, 580
The factors of 192 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192
The HCF of 77,580,192 is 1.
Lets's calculate GCF of 77,580,192
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 77
:1,7,11,77
Now, list down the factors of 580
:1,2,4,5,10,20,29,58,116,145,290,580
Now, list down the factors of 192
:1,2,3,4,6,8,12,16,24,32,48,64,96,192
Greatest Common Factor
We found the factors 77,580,192 . The biggest common factor number is the GCF number.
So the greatest common factor 77,580,192 is 1.
Lets's calculate LCM of 19,72,132
2 | 19, 72, 132 |
2 | 19, 36, 66 |
3 | 19, 18, 33 |
19, 6, 11 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 19 x 6 x 11 = 15048
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/15048
Therefore, the GCF of Fractions 77/19,580/72,192/132 is 1/15048
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 19,72,132 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(19,72,132) = 1
common factors(in case of two or more numbers have common factors) = 12
GCF(19,72,132) x common factors =1 x 12 = 12
LCM(19,72,132) = ( 19 × 72 × 132 ) / 12
LCM(19,72,132) = 180576 / 12
LCM(19,72,132) = 15048
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 77,580,192?
The HCF of 77,580,192 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 77/19, 580/72, 192/132?
Answer: GCF of Numerators as per given numbers 77/19, 580/72, 192/132 is
GCF of Numerators i.e. for 77,580,192 is 1
LCM of denominators i.e. for 19,72,132 is 15048.
Thus, GCF of Fractions is 1/15048.Finally, GCF of Fractions for 77/19, 580/72, 192/132 is 1/15048.