GCF of 60/84, 69/13, 384/388
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 60/84, 69/13, 384/388 i.e 3/105924 easily. The following is the detailed procedure to determine the greatest common factor of fractions 60/84, 69/13, 384/388.
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 60/84,69/13,384/388?
Given fractions are 60/84,69/13,384/388
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 60/84,69/13,384/388, numerators are 60,69,384
Denominators are 84,13,388
The GCF of 60,69,384 is 3 .
LCM of 84,13,388 is 105924.
The greatest common factor of 60/84,69/13,384/388 = [GCF of 60,69,384]/[LCM of 84,13,388]= 3/105924
Therefore, the GCF of 60/84,69/13,384/388 is 3/105924.
To find the highest common factor of 60,69,384, we have to find the factors of both numbers and list the highest common factor.
The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
The factors of 69 are 1, 3, 23, 69
The factors of 384 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 384
The HCF of 60,69,384 is 3.
Lets's calculate GCF of 60,69,384
| 3 | 60, 69, 384 |
| 20, 23, 128 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 60,69,384 By Matching Biggest Common Factor Method
Now, list down the factors of 60
:1,2,3,4,5,6,10,12,15,20,30,60
Now, list down the factors of 69
:1,3,23,69
Now, list down the factors of 384
:1,2,3,4,6,8,12,16,24,32,48,64,96,128,192,384
Greatest Common Factor
We found the factors 60,69,384 . The biggest common factor number is the GCF number.
So the greatest common factor 60,69,384 is 3.
Lets's calculate LCM of 84,13,388
| 2 | 84, 13, 388 |
| 2 | 42, 13, 194 |
| 21, 13, 97 |
∴ So the LCM of the given numbers is 2 x 2 x 21 x 13 x 97 = 105924
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/105924
Therefore, the GCF of Fractions 60/84,69/13,384/388 is 3/105924
Least Common Multiple of 84,13,388 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 84,13,388 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(84,13,388) = 1
common factors(in case of two or more numbers have common factors) = 4
GCF(84,13,388) x common factors =1 x 4 = 4
LCM(84,13,388) = ( 84 × 13 × 388 ) / 4
LCM(84,13,388) = 423696 / 4
LCM(84,13,388) = 105924
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FAQs on GCF of Fractions of 60/84, 69/13, 384/388
1. What is the HCF of 60,69,384?
The HCF of 60,69,384 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 60/84, 69/13, 384/388?
Answer: GCF of Numerators as per given numbers 60/84, 69/13, 384/388 is
GCF of Numerators i.e. for 60,69,384 is 3
LCM of denominators i.e. for 84,13,388 is 105924.
Thus, GCF of Fractions is 3/105924.Finally, GCF of Fractions for 60/84, 69/13, 384/388 is 3/105924.