GCF of 12/12, 30/30, 144/72
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 12/12, 30/30, 144/72 i.e 6/360 easily. The following is the detailed procedure to determine the greatest common factor of fractions 12/12, 30/30, 144/72.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
What is the GCF of 12/12,30/30,144/72?
Given fractions are 12/12,30/30,144/72
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 12/12,30/30,144/72, numerators are 12,30,144
Denominators are 12,30,72
The GCF of 12,30,144 is 6 .
LCM of 12,30,72 is 360.
The greatest common factor of 12/12,30/30,144/72 = [GCF of 12,30,144]/[LCM of 12,30,72]= 6/360
Therefore, the GCF of 12/12,30/30,144/72 is 6/360.
To find the highest common factor of 12,30,144, we have to find the factors of both numbers and list the highest common factor.
The factors of 12 are 1, 2, 3, 4, 6, 12
The factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30
The factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
The HCF of 12,30,144 is 6.
Lets's calculate GCF of 12,30,144
| 2 | 12, 30, 144 |
| 3 | 6, 15, 72 |
| 2, 5, 24 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Greatest Common Factor of 12,30,144 By Matching Biggest Common Factor Method
Now, list down the factors of 12
:1,2,3,4,6,12
Now, list down the factors of 30
:1,2,3,5,6,10,15,30
Now, list down the factors of 144
:1,2,3,4,6,8,9,12,16,18,24,36,48,72,144
Greatest Common Factor
We found the factors 12,30,144 . The biggest common factor number is the GCF number.
So the greatest common factor 12,30,144 is 6.
Lets's calculate LCM of 12,30,72
| 2 | 12, 30, 72 |
| 2 | 6, 15, 36 |
| 3 | 3, 15, 18 |
| 1, 5, 6 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 1 x 5 x 6 = 360
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/360
Therefore, the GCF of Fractions 12/12,30/30,144/72 is 6/360
Least Common Multiple of 12,30,72 with GCF Formula
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 12,30,72 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(12,30,72) = 6
common factors(in case of two or more numbers have common factors) = 12
GCF(12,30,72) x common factors =6 x 12 = 72
LCM(12,30,72) = ( 12 × 30 × 72 ) / 72
LCM(12,30,72) = 25920 / 72
LCM(12,30,72) = 360
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 12/12, 30/30, 144/72
1. What is the HCF of 12,30,144?
The HCF of 12,30,144 is 6
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 12/12, 30/30, 144/72?
Answer: GCF of Numerators as per given numbers 12/12, 30/30, 144/72 is
GCF of Numerators i.e. for 12,30,144 is 6
LCM of denominators i.e. for 12,30,72 is 360.
Thus, GCF of Fractions is 6/360.Finally, GCF of Fractions for 12/12, 30/30, 144/72 is 6/360.