Use our free GCF of Fractions Calculator tool to compute the GCF of 20/75, 36/75, 272/19 i.e 4/1425 easily. The following is the detailed procedure to determine the greatest common factor of fractions 20/75, 36/75, 272/19.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 20/75,36/75,272/19
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 20/75,36/75,272/19, numerators are 20,36,272
Denominators are 75,75,19
The GCF of 20,36,272 is 4 .
LCM of 75,75,19 is 1425.
The greatest common factor of 20/75,36/75,272/19 = [GCF of 20,36,272]/[LCM of 75,75,19]= 4/1425
Therefore, the GCF of 20/75,36/75,272/19 is 4/1425.
To find the highest common factor of 20,36,272, we have to find the factors of both numbers and list the highest common factor.
The factors of 20 are 1, 2, 4, 5, 10, 20
The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36
The factors of 272 are 1, 2, 4, 8, 16, 17, 34, 68, 136, 272
The HCF of 20,36,272 is 4.
Lets's calculate GCF of 20,36,272
2 | 20, 36, 272 |
2 | 10, 18, 136 |
5, 9, 68 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Now, list down the factors of 20
:1,2,4,5,10,20
Now, list down the factors of 36
:1,2,3,4,6,9,12,18,36
Now, list down the factors of 272
:1,2,4,8,16,17,34,68,136,272
Greatest Common Factor
We found the factors 20,36,272 . The biggest common factor number is the GCF number.
So the greatest common factor 20,36,272 is 4.
Lets's calculate LCM of 75,75,19
3 | 75, 75, 19 |
5 | 25, 25, 19 |
5 | 5, 5, 19 |
1, 1, 19 |
∴ So the LCM of the given numbers is 3 x 5 x 5 x 1 x 1 x 19 = 1425
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/1425
Therefore, the GCF of Fractions 20/75,36/75,272/19 is 4/1425
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 75,75,19 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(75,75,19) = 1
common factors(in case of two or more numbers have common factors) = 75
GCF(75,75,19) x common factors =1 x 75 = 75
LCM(75,75,19) = ( 75 × 75 × 19 ) / 75
LCM(75,75,19) = 106875 / 75
LCM(75,75,19) = 1425
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 20,36,272?
The HCF of 20,36,272 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 20/75, 36/75, 272/19?
Answer: GCF of Numerators as per given numbers 20/75, 36/75, 272/19 is
GCF of Numerators i.e. for 20,36,272 is 4
LCM of denominators i.e. for 75,75,19 is 1425.
Thus, GCF of Fractions is 4/1425.Finally, GCF of Fractions for 20/75, 36/75, 272/19 is 4/1425.