GCF of 7209/305, 9312/4862
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7209/305, 9312/4862 i.e 3/1482910 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7209/305, 9312/4862.
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 7209/305,9312/4862?
Given fractions are 7209/305,9312/4862
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 7209/305,9312/4862, numerators are 7209,9312
Denominators are 305,4862
The GCF of 7209,9312 is 3 .
LCM of 305,4862 is 1482910.
The greatest common factor of 7209/305,9312/4862 = [GCF of 7209,9312]/[LCM of 305,4862]= 3/1482910
Therefore, the GCF of 7209/305,9312/4862 is 3/1482910.
To find the highest common factor of 7209,9312, we have to find the factors of both numbers and list the highest common factor.
The factors of 7209 are 1, 3, 9, 27, 81, 89, 267, 801, 2403, 7209
The factors of 9312 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 97, 194, 291, 388, 582, 776, 1164, 1552, 2328, 3104, 4656, 9312
The HCF of 7209,9312 is 3.
Lets's calculate GCF of 7209,9312
| 3 | 7209, 9312 |
| 2403, 3104 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 7209,9312 By Matching Biggest Common Factor Method
Now, list down the factors of 7209
:1,3,9,27,81,89,267,801,2403,7209
Now, list down the factors of 9312
:1,2,3,4,6,8,12,16,24,32,48,96,97,194,291,388,582,776,1164,1552,2328,3104,4656,9312
Greatest Common Factor
We found the factors 7209,9312 . The biggest common factor number is the GCF number.
So the greatest common factor 7209,9312 is 3.
Lets's calculate LCM of 305,4862
Given numbers has no common factors except 1. So, there LCM is their product i.e 1482910
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/1482910
Therefore, the GCF of Fractions 7209/305,9312/4862 is 3/1482910
Least Common Multiple of 305,4862 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 305,4862 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(305,4862) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(305,4862) x common factors =1 x 1 = 1
LCM(305,4862) = ( 305 × 4862 ) / 1
LCM(305,4862) = 1482910 / 1
LCM(305,4862) = 1482910
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FAQs on GCF of Fractions of 7209/305, 9312/4862
1. What is the HCF of 7209,9312?
The HCF of 7209,9312 is 3
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 7209/305, 9312/4862?
Answer: GCF of Numerators as per given numbers 7209/305, 9312/4862 is
GCF of Numerators i.e. for 7209,9312 is 3
LCM of denominators i.e. for 305,4862 is 1482910.
Thus, GCF of Fractions is 3/1482910.Finally, GCF of Fractions for 7209/305, 9312/4862 is 3/1482910.