GCF of 312/76, 198/407
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 312/76, 198/407 i.e 6/30932 easily. The following is the detailed procedure to determine the greatest common factor of fractions 312/76, 198/407.
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 312/76,198/407?
Given fractions are 312/76,198/407
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 312/76,198/407, numerators are 312,198
Denominators are 76,407
The GCF of 312,198 is 6 .
LCM of 76,407 is 30932.
The greatest common factor of 312/76,198/407 = [GCF of 312,198]/[LCM of 76,407]= 6/30932
Therefore, the GCF of 312/76,198/407 is 6/30932.
To find the highest common factor of 312,198, 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 198 are 1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, 198
The HCF of 312,198 is 6.
Lets's calculate GCF of 312,198
| 2 | 312, 198 |
| 3 | 156, 99 |
| 52, 33 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Greatest Common Factor of 312,198 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 198
:1,2,3,6,9,11,18,22,33,66,99,198
Greatest Common Factor
We found the factors 312,198 . The biggest common factor number is the GCF number.
So the greatest common factor 312,198 is 6.
Lets's calculate LCM of 76,407
Given numbers has no common factors except 1. So, there LCM is their product i.e 30932
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/30932
Therefore, the GCF of Fractions 312/76,198/407 is 6/30932
Least Common Multiple of 76,407 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 76,407 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(76,407) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(76,407) x common factors =1 x 1 = 1
LCM(76,407) = ( 76 × 407 ) / 1
LCM(76,407) = 30932 / 1
LCM(76,407) = 30932
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FAQs on GCF of Fractions of 312/76, 198/407
1. What is the HCF of 312,198?
The HCF of 312,198 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 312/76, 198/407?
Answer: GCF of Numerators as per given numbers 312/76, 198/407 is
GCF of Numerators i.e. for 312,198 is 6
LCM of denominators i.e. for 76,407 is 30932.
Thus, GCF of Fractions is 6/30932.Finally, GCF of Fractions for 312/76, 198/407 is 6/30932.