GCF of 16/30, 24/60, 32/75, 36/120
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 16/30, 24/60, 32/75, 36/120 i.e 4/600 easily. The following is the detailed procedure to determine the greatest common factor of fractions 16/30, 24/60, 32/75, 36/120.
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 16/30,24/60,32/75,36/120?
Given fractions are 16/30,24/60,32/75,36/120
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 16/30,24/60,32/75,36/120, numerators are 16,24,32,36
Denominators are 30,60,75,120
The GCF of 16,24,32,36 is 4 .
LCM of 30,60,75,120 is 600.
The greatest common factor of 16/30,24/60,32/75,36/120 = [GCF of 16,24,32,36]/[LCM of 30,60,75,120]= 4/600
Therefore, the GCF of 16/30,24/60,32/75,36/120 is 4/600.
To find the highest common factor of 16,24,32,36, we have to find the factors of both numbers and list the highest common factor.
The factors of 16 are 1, 2, 4, 8, 16
The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24
The factors of 32 are 1, 2, 4, 8, 16, 32
The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36
The HCF of 16,24,32,36 is 4.
Lets's calculate GCF of 16,24,32,36
| 2 | 16, 24, 32, 36 |
| 2 | 8, 12, 16, 18 |
| 4, 6, 8, 9 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Greatest Common Factor of 16,24,32,36 By Matching Biggest Common Factor Method
Now, list down the factors of 16
:1,2,4,8,16
Now, list down the factors of 24
:1,2,3,4,6,8,12,24
Now, list down the factors of 32
:1,2,4,8,16,32
Now, list down the factors of 36
:1,2,3,4,6,9,12,18,36
Greatest Common Factor
We found the factors 16,24,32,36 . The biggest common factor number is the GCF number.
So the greatest common factor 16,24,32,36 is 4.
Lets's calculate LCM of 30,60,75,120
| 2 | 30, 60, 75, 120 |
| 2 | 15, 30, 75, 60 |
| 3 | 15, 15, 75, 30 |
| 5 | 5, 5, 25, 10 |
| 1, 1, 5, 2 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 5 x 1 x 1 x 5 x 2 = 600
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/600
Therefore, the GCF of Fractions 16/30,24/60,32/75,36/120 is 4/600
Least Common Multiple of 30,60,75,120 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 30,60,75,120 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(30,60,75,120) = 15
common factors(in case of two or more numbers have common factors) = 1800
GCF(30,60,75,120) x common factors =15 x 1800 = 27000
LCM(30,60,75,120) = ( 30 × 60 × 75 × 120 ) / 27000
LCM(30,60,75,120) = 16200000 / 27000
LCM(30,60,75,120) = 600
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 16/30, 24/60, 32/75, 36/120
1. What is the HCF of 16,24,32,36?
The HCF of 16,24,32,36 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 16/30, 24/60, 32/75, 36/120?
Answer: GCF of Numerators as per given numbers 16/30, 24/60, 32/75, 36/120 is
GCF of Numerators i.e. for 16,24,32,36 is 4
LCM of denominators i.e. for 30,60,75,120 is 600.
Thus, GCF of Fractions is 4/600.Finally, GCF of Fractions for 16/30, 24/60, 32/75, 36/120 is 4/600.