GCF of 33/21, 63/16, 78/41, 57/54
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 33/21, 63/16, 78/41, 57/54 i.e 3/123984 easily. The following is the detailed procedure to determine the greatest common factor of fractions 33/21, 63/16, 78/41, 57/54.
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 33/21,63/16,78/41,57/54?
Given fractions are 33/21,63/16,78/41,57/54
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 33/21,63/16,78/41,57/54, numerators are 33,63,78,57
Denominators are 21,16,41,54
The GCF of 33,63,78,57 is 3 .
LCM of 21,16,41,54 is 123984.
The greatest common factor of 33/21,63/16,78/41,57/54 = [GCF of 33,63,78,57]/[LCM of 21,16,41,54]= 3/123984
Therefore, the GCF of 33/21,63/16,78/41,57/54 is 3/123984.
To find the highest common factor of 33,63,78,57, we have to find the factors of both numbers and list the highest common factor.
The factors of 33 are 1, 3, 11, 33
The factors of 63 are 1, 3, 7, 9, 21, 63
The factors of 78 are 1, 2, 3, 6, 13, 26, 39, 78
The factors of 57 are 1, 3, 19, 57
The HCF of 33,63,78,57 is 3.
Lets's calculate GCF of 33,63,78,57
| 3 | 33, 63, 78, 57 |
| 11, 21, 26, 19 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 33,63,78,57 By Matching Biggest Common Factor Method
Now, list down the factors of 33
:1,3,11,33
Now, list down the factors of 63
:1,3,7,9,21,63
Now, list down the factors of 78
:1,2,3,6,13,26,39,78
Now, list down the factors of 57
:1,3,19,57
Greatest Common Factor
We found the factors 33,63,78,57 . The biggest common factor number is the GCF number.
So the greatest common factor 33,63,78,57 is 3.
Lets's calculate LCM of 21,16,41,54
| 2 | 21, 16, 41, 54 |
| 3 | 21, 8, 41, 27 |
| 7, 8, 41, 9 |
∴ So the LCM of the given numbers is 2 x 3 x 7 x 8 x 41 x 9 = 123984
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/123984
Therefore, the GCF of Fractions 33/21,63/16,78/41,57/54 is 3/123984
Least Common Multiple of 21,16,41,54 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 21,16,41,54 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(21,16,41,54) = 1
common factors(in case of two or more numbers have common factors) = 6
GCF(21,16,41,54) x common factors =1 x 6 = 6
LCM(21,16,41,54) = ( 21 × 16 × 41 × 54 ) / 6
LCM(21,16,41,54) = 743904 / 6
LCM(21,16,41,54) = 123984
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 33/21, 63/16, 78/41, 57/54
1. What is the HCF of 33,63,78,57?
The HCF of 33,63,78,57 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 33/21, 63/16, 78/41, 57/54?
Answer: GCF of Numerators as per given numbers 33/21, 63/16, 78/41, 57/54 is
GCF of Numerators i.e. for 33,63,78,57 is 3
LCM of denominators i.e. for 21,16,41,54 is 123984.
Thus, GCF of Fractions is 3/123984.Finally, GCF of Fractions for 33/21, 63/16, 78/41, 57/54 is 3/123984.