GCF of 312/324, 299/108
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 312/324, 299/108 i.e 13/324 easily. The following is the detailed procedure to determine the greatest common factor of fractions 312/324, 299/108.
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 312/324,299/108?
Given fractions are 312/324,299/108
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 312/324,299/108, numerators are 312,299
Denominators are 324,108
The GCF of 312,299 is 13 .
LCM of 324,108 is 324.
The greatest common factor of 312/324,299/108 = [GCF of 312,299]/[LCM of 324,108]= 13/324
Therefore, the GCF of 312/324,299/108 is 13/324.
To find the highest common factor of 312,299, we have to find the factors of both numbers and list the highest common factor.
The factors of 312 are 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312
The factors of 299 are 1, 13, 23, 299
The HCF of 312,299 is 13.
Lets's calculate GCF of 312,299
| 13 | 312, 299 |
| 24, 23 |
∴ So the GCF of the given numbers is 13 = 13
Greatest Common Factor of 312,299 By Matching Biggest Common Factor Method
Now, list down the factors of 312
:1,2,3,4,6,8,12,13,24,26,39,52,78,104,156,312
Now, list down the factors of 299
:1,13,23,299
Greatest Common Factor
We found the factors 312,299 . The biggest common factor number is the GCF number.
So the greatest common factor 312,299 is 13.
Lets's calculate LCM of 324,108
| 2 | 324, 108 |
| 2 | 162, 54 |
| 3 | 81, 27 |
| 3 | 9, 27 |
| 3 | 3, 9 |
| 1, 3 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 3 x 3 x 1 x 3 = 324
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 13/324
Therefore, the GCF of Fractions 312/324,299/108 is 13/324
Least Common Multiple of 324,108 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 324,108 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(324,108) = 108
common factors(in case of two or more numbers have common factors) = 1
GCF(324,108) x common factors =108 x 1 = 108
LCM(324,108) = ( 324 × 108 ) / 108
LCM(324,108) = 34992 / 108
LCM(324,108) = 324
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FAQs on GCF of Fractions of 312/324, 299/108
1. What is the HCF of 312,299?
The HCF of 312,299 is 13
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 312/324, 299/108?
Answer: GCF of Numerators as per given numbers 312/324, 299/108 is
GCF of Numerators i.e. for 312,299 is 13
LCM of denominators i.e. for 324,108 is 324.
Thus, GCF of Fractions is 13/324.Finally, GCF of Fractions for 312/324, 299/108 is 13/324.