GCF of 684/180, 309/365
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 684/180, 309/365 i.e 3/13140 easily. The following is the detailed procedure to determine the greatest common factor of fractions 684/180, 309/365.
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 684/180,309/365?
Given fractions are 684/180,309/365
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 684/180,309/365, numerators are 684,309
Denominators are 180,365
The GCF of 684,309 is 3 .
LCM of 180,365 is 13140.
The greatest common factor of 684/180,309/365 = [GCF of 684,309]/[LCM of 180,365]= 3/13140
Therefore, the GCF of 684/180,309/365 is 3/13140.
To find the highest common factor of 684,309, we have to find the factors of both numbers and list the highest common factor.
The factors of 684 are 1, 2, 3, 4, 6, 9, 12, 18, 19, 36, 38, 57, 76, 114, 171, 228, 342, 684
The factors of 309 are 1, 3, 103, 309
The HCF of 684,309 is 3.
Lets's calculate GCF of 684,309
| 3 | 684, 309 |
| 228, 103 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 684,309 By Matching Biggest Common Factor Method
Now, list down the factors of 684
:1,2,3,4,6,9,12,18,19,36,38,57,76,114,171,228,342,684
Now, list down the factors of 309
:1,3,103,309
Greatest Common Factor
We found the factors 684,309 . The biggest common factor number is the GCF number.
So the greatest common factor 684,309 is 3.
Lets's calculate LCM of 180,365
| 5 | 180, 365 |
| 36, 73 |
∴ So the LCM of the given numbers is 5 x 36 x 73 = 13140
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/13140
Therefore, the GCF of Fractions 684/180,309/365 is 3/13140
Least Common Multiple of 180,365 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 180,365 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(180,365) = 5
common factors(in case of two or more numbers have common factors) = 1
GCF(180,365) x common factors =5 x 1 = 5
LCM(180,365) = ( 180 × 365 ) / 5
LCM(180,365) = 65700 / 5
LCM(180,365) = 13140
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FAQs on GCF of Fractions of 684/180, 309/365
1. What is the HCF of 684,309?
The HCF of 684,309 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 684/180, 309/365?
Answer: GCF of Numerators as per given numbers 684/180, 309/365 is
GCF of Numerators i.e. for 684,309 is 3
LCM of denominators i.e. for 180,365 is 13140.
Thus, GCF of Fractions is 3/13140.Finally, GCF of Fractions for 684/180, 309/365 is 3/13140.