GCF of 542/55, 202/90, 405/132
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 542/55, 202/90, 405/132 i.e 1/1980 easily. The following is the detailed procedure to determine the greatest common factor of fractions 542/55, 202/90, 405/132.
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 542/55,202/90,405/132?
Given fractions are 542/55,202/90,405/132
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 542/55,202/90,405/132, numerators are 542,202,405
Denominators are 55,90,132
The GCF of 542,202,405 is 1 .
LCM of 55,90,132 is 1980.
The greatest common factor of 542/55,202/90,405/132 = [GCF of 542,202,405]/[LCM of 55,90,132]= 1/1980
Therefore, the GCF of 542/55,202/90,405/132 is 1/1980.
To find the highest common factor of 542,202,405, we have to find the factors of both numbers and list the highest common factor.
The factors of 542 are 1, 2, 271, 542
The factors of 202 are 1, 2, 101, 202
The factors of 405 are 1, 3, 5, 9, 15, 27, 45, 81, 135, 405
The HCF of 542,202,405 is 1.
Lets's calculate GCF of 542,202,405
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 542,202,405 By Matching Biggest Common Factor Method
Now, list down the factors of 542
:1,2,271,542
Now, list down the factors of 202
:1,2,101,202
Now, list down the factors of 405
:1,3,5,9,15,27,45,81,135,405
Greatest Common Factor
We found the factors 542,202,405 . The biggest common factor number is the GCF number.
So the greatest common factor 542,202,405 is 1.
Lets's calculate LCM of 55,90,132
| 2 | 55, 90, 132 |
| 3 | 55, 45, 66 |
| 5 | 55, 15, 22 |
| 11 | 11, 3, 22 |
| 1, 3, 2 |
∴ So the LCM of the given numbers is 2 x 3 x 5 x 11 x 1 x 3 x 2 = 1980
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1980
Therefore, the GCF of Fractions 542/55,202/90,405/132 is 1/1980
Least Common Multiple of 55,90,132 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 55,90,132 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(55,90,132) = 1
common factors(in case of two or more numbers have common factors) = 330
GCF(55,90,132) x common factors =1 x 330 = 330
LCM(55,90,132) = ( 55 × 90 × 132 ) / 330
LCM(55,90,132) = 653400 / 330
LCM(55,90,132) = 1980
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FAQs on GCF of Fractions of 542/55, 202/90, 405/132
1. What is the HCF of 542,202,405?
The HCF of 542,202,405 is 1
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 542/55, 202/90, 405/132?
Answer: GCF of Numerators as per given numbers 542/55, 202/90, 405/132 is
GCF of Numerators i.e. for 542,202,405 is 1
LCM of denominators i.e. for 55,90,132 is 1980.
Thus, GCF of Fractions is 1/1980.Finally, GCF of Fractions for 542/55, 202/90, 405/132 is 1/1980.