GCF of 3084/348, 9288/540
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 3084/348, 9288/540 i.e 12/15660 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3084/348, 9288/540.
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 3084/348,9288/540?
Given fractions are 3084/348,9288/540
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 3084/348,9288/540, numerators are 3084,9288
Denominators are 348,540
The GCF of 3084,9288 is 12 .
LCM of 348,540 is 15660.
The greatest common factor of 3084/348,9288/540 = [GCF of 3084,9288]/[LCM of 348,540]= 12/15660
Therefore, the GCF of 3084/348,9288/540 is 12/15660.
To find the highest common factor of 3084,9288, we have to find the factors of both numbers and list the highest common factor.
The factors of 3084 are 1, 2, 3, 4, 6, 12, 257, 514, 771, 1028, 1542, 3084
The factors of 9288 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 43, 54, 72, 86, 108, 129, 172, 216, 258, 344, 387, 516, 774, 1032, 1161, 1548, 2322, 3096, 4644, 9288
The HCF of 3084,9288 is 12.
Lets's calculate GCF of 3084,9288
| 2 | 3084, 9288 |
| 2 | 1542, 4644 |
| 3 | 771, 2322 |
| 257, 774 |
∴ So the GCF of the given numbers is 2 x 2 x 3 = 12
Greatest Common Factor of 3084,9288 By Matching Biggest Common Factor Method
Now, list down the factors of 3084
:1,2,3,4,6,12,257,514,771,1028,1542,3084
Now, list down the factors of 9288
:1,2,3,4,6,8,9,12,18,24,27,36,43,54,72,86,108,129,172,216,258,344,387,516,774,1032,1161,1548,2322,3096,4644,9288
Greatest Common Factor
We found the factors 3084,9288 . The biggest common factor number is the GCF number.
So the greatest common factor 3084,9288 is 12.
Lets's calculate LCM of 348,540
| 2 | 348, 540 |
| 2 | 174, 270 |
| 3 | 87, 135 |
| 29, 45 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 29 x 45 = 15660
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 12/15660
Therefore, the GCF of Fractions 3084/348,9288/540 is 12/15660
Least Common Multiple of 348,540 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 348,540 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(348,540) = 12
common factors(in case of two or more numbers have common factors) = 1
GCF(348,540) x common factors =12 x 1 = 12
LCM(348,540) = ( 348 × 540 ) / 12
LCM(348,540) = 187920 / 12
LCM(348,540) = 15660
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FAQs on GCF of Fractions of 3084/348, 9288/540
1. What is the HCF of 3084,9288?
The HCF of 3084,9288 is 12
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 3084/348, 9288/540?
Answer: GCF of Numerators as per given numbers 3084/348, 9288/540 is
GCF of Numerators i.e. for 3084,9288 is 12
LCM of denominators i.e. for 348,540 is 15660.
Thus, GCF of Fractions is 12/15660.Finally, GCF of Fractions for 3084/348, 9288/540 is 12/15660.