Use our free GCF of Fractions Calculator tool to compute the GCF of 60/29, 38/68, 120/72 i.e 2/35496 easily. The following is the detailed procedure to determine the greatest common factor of fractions 60/29, 38/68, 120/72.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 60/29,38/68,120/72
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 60/29,38/68,120/72, numerators are 60,38,120
Denominators are 29,68,72
The GCF of 60,38,120 is 2 .
LCM of 29,68,72 is 35496.
The greatest common factor of 60/29,38/68,120/72 = [GCF of 60,38,120]/[LCM of 29,68,72]= 2/35496
Therefore, the GCF of 60/29,38/68,120/72 is 2/35496.
To find the highest common factor of 60,38,120, we have to find the factors of both numbers and list the highest common factor.
The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
The factors of 38 are 1, 2, 19, 38
The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
The HCF of 60,38,120 is 2.
Lets's calculate GCF of 60,38,120
2 | 60, 38, 120 |
30, 19, 60 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 60
:1,2,3,4,5,6,10,12,15,20,30,60
Now, list down the factors of 38
:1,2,19,38
Now, list down the factors of 120
:1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120
Greatest Common Factor
We found the factors 60,38,120 . The biggest common factor number is the GCF number.
So the greatest common factor 60,38,120 is 2.
Lets's calculate LCM of 29,68,72
2 | 29, 68, 72 |
2 | 29, 34, 36 |
29, 17, 18 |
∴ So the LCM of the given numbers is 2 x 2 x 29 x 17 x 18 = 35496
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/35496
Therefore, the GCF of Fractions 60/29,38/68,120/72 is 2/35496
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 29,68,72 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(29,68,72) = 1
common factors(in case of two or more numbers have common factors) = 4
GCF(29,68,72) x common factors =1 x 4 = 4
LCM(29,68,72) = ( 29 × 68 × 72 ) / 4
LCM(29,68,72) = 141984 / 4
LCM(29,68,72) = 35496
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 60,38,120?
The HCF of 60,38,120 is 2
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 60/29, 38/68, 120/72?
Answer: GCF of Numerators as per given numbers 60/29, 38/68, 120/72 is
GCF of Numerators i.e. for 60,38,120 is 2
LCM of denominators i.e. for 29,68,72 is 35496.
Thus, GCF of Fractions is 2/35496.Finally, GCF of Fractions for 60/29, 38/68, 120/72 is 2/35496.