GCF of 324/27, 104/55, 378/70
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 324/27, 104/55, 378/70 i.e 2/20790 easily. The following is the detailed procedure to determine the greatest common factor of fractions 324/27, 104/55, 378/70.
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 324/27,104/55,378/70?
Given fractions are 324/27,104/55,378/70
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 324/27,104/55,378/70, numerators are 324,104,378
Denominators are 27,55,70
The GCF of 324,104,378 is 2 .
LCM of 27,55,70 is 20790.
The greatest common factor of 324/27,104/55,378/70 = [GCF of 324,104,378]/[LCM of 27,55,70]= 2/20790
Therefore, the GCF of 324/27,104/55,378/70 is 2/20790.
To find the highest common factor of 324,104,378, we have to find the factors of both numbers and list the highest common factor.
The factors of 324 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 324
The factors of 104 are 1, 2, 4, 8, 13, 26, 52, 104
The factors of 378 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189, 378
The HCF of 324,104,378 is 2.
Lets's calculate GCF of 324,104,378
| 2 | 324, 104, 378 |
| 162, 52, 189 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 324,104,378 By Matching Biggest Common Factor Method
Now, list down the factors of 324
:1,2,3,4,6,9,12,18,27,36,54,81,108,162,324
Now, list down the factors of 104
:1,2,4,8,13,26,52,104
Now, list down the factors of 378
:1,2,3,6,7,9,14,18,21,27,42,54,63,126,189,378
Greatest Common Factor
We found the factors 324,104,378 . The biggest common factor number is the GCF number.
So the greatest common factor 324,104,378 is 2.
Lets's calculate LCM of 27,55,70
| 5 | 27, 55, 70 |
| 27, 11, 14 |
∴ So the LCM of the given numbers is 5 x 27 x 11 x 14 = 20790
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/20790
Therefore, the GCF of Fractions 324/27,104/55,378/70 is 2/20790
Least Common Multiple of 27,55,70 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 27,55,70 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(27,55,70) = 1
common factors(in case of two or more numbers have common factors) = 5
GCF(27,55,70) x common factors =1 x 5 = 5
LCM(27,55,70) = ( 27 × 55 × 70 ) / 5
LCM(27,55,70) = 103950 / 5
LCM(27,55,70) = 20790
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FAQs on GCF of Fractions of 324/27, 104/55, 378/70
1. What is the HCF of 324,104,378?
The HCF of 324,104,378 is 2
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 324/27, 104/55, 378/70?
Answer: GCF of Numerators as per given numbers 324/27, 104/55, 378/70 is
GCF of Numerators i.e. for 324,104,378 is 2
LCM of denominators i.e. for 27,55,70 is 20790.
Thus, GCF of Fractions is 2/20790.Finally, GCF of Fractions for 324/27, 104/55, 378/70 is 2/20790.