GCF of 99/16, 27/69, 30/14, 85/12
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 99/16, 27/69, 30/14, 85/12 i.e 1/7728 easily. The following is the detailed procedure to determine the greatest common factor of fractions 99/16, 27/69, 30/14, 85/12.
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 99/16,27/69,30/14,85/12?
Given fractions are 99/16,27/69,30/14,85/12
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 99/16,27/69,30/14,85/12, numerators are 99,27,30,85
Denominators are 16,69,14,12
The GCF of 99,27,30,85 is 1 .
LCM of 16,69,14,12 is 7728.
The greatest common factor of 99/16,27/69,30/14,85/12 = [GCF of 99,27,30,85]/[LCM of 16,69,14,12]= 1/7728
Therefore, the GCF of 99/16,27/69,30/14,85/12 is 1/7728.
To find the highest common factor of 99,27,30,85, we have to find the factors of both numbers and list the highest common factor.
The factors of 99 are 1, 3, 9, 11, 33, 99
The factors of 27 are 1, 3, 9, 27
The factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30
The factors of 85 are 1, 5, 17, 85
The HCF of 99,27,30,85 is 1.
Lets's calculate GCF of 99,27,30,85
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 99,27,30,85 By Matching Biggest Common Factor Method
Now, list down the factors of 99
:1,3,9,11,33,99
Now, list down the factors of 27
:1,3,9,27
Now, list down the factors of 30
:1,2,3,5,6,10,15,30
Now, list down the factors of 85
:1,5,17,85
Greatest Common Factor
We found the factors 99,27,30,85 . The biggest common factor number is the GCF number.
So the greatest common factor 99,27,30,85 is 1.
Lets's calculate LCM of 16,69,14,12
| 2 | 16, 69, 14, 12 |
| 2 | 8, 69, 7, 6 |
| 3 | 4, 69, 7, 3 |
| 4, 23, 7, 1 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 4 x 23 x 7 x 1 = 7728
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/7728
Therefore, the GCF of Fractions 99/16,27/69,30/14,85/12 is 1/7728
Least Common Multiple of 16,69,14,12 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 16,69,14,12 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(16,69,14,12) = 1
common factors(in case of two or more numbers have common factors) = 24
GCF(16,69,14,12) x common factors =1 x 24 = 24
LCM(16,69,14,12) = ( 16 × 69 × 14 × 12 ) / 24
LCM(16,69,14,12) = 185472 / 24
LCM(16,69,14,12) = 7728
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 99/16, 27/69, 30/14, 85/12
1. What is the HCF of 99,27,30,85?
The HCF of 99,27,30,85 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 99/16, 27/69, 30/14, 85/12?
Answer: GCF of Numerators as per given numbers 99/16, 27/69, 30/14, 85/12 is
GCF of Numerators i.e. for 99,27,30,85 is 1
LCM of denominators i.e. for 16,69,14,12 is 7728.
Thus, GCF of Fractions is 1/7728.Finally, GCF of Fractions for 99/16, 27/69, 30/14, 85/12 is 1/7728.