GCF of 202/285, 405/120
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 202/285, 405/120 i.e 1/2280 easily. The following is the detailed procedure to determine the greatest common factor of fractions 202/285, 405/120.
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 202/285,405/120?
Given fractions are 202/285,405/120
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 202/285,405/120, numerators are 202,405
Denominators are 285,120
The GCF of 202,405 is 1 .
LCM of 285,120 is 2280.
The greatest common factor of 202/285,405/120 = [GCF of 202,405]/[LCM of 285,120]= 1/2280
Therefore, the GCF of 202/285,405/120 is 1/2280.
To find the highest common factor of 202,405, we have to find the factors of both numbers and list the highest common factor.
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 202,405 is 1.
Lets's calculate GCF of 202,405
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 202,405 By Matching Biggest Common Factor Method
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 202,405 . The biggest common factor number is the GCF number.
So the greatest common factor 202,405 is 1.
Lets's calculate LCM of 285,120
| 3 | 285, 120 |
| 5 | 95, 40 |
| 19, 8 |
∴ So the LCM of the given numbers is 3 x 5 x 19 x 8 = 2280
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2280
Therefore, the GCF of Fractions 202/285,405/120 is 1/2280
Least Common Multiple of 285,120 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 285,120 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(285,120) = 15
common factors(in case of two or more numbers have common factors) = 1
GCF(285,120) x common factors =15 x 1 = 15
LCM(285,120) = ( 285 × 120 ) / 15
LCM(285,120) = 34200 / 15
LCM(285,120) = 2280
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FAQs on GCF of Fractions of 202/285, 405/120
1. What is the HCF of 202,405?
The HCF of 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 202/285, 405/120?
Answer: GCF of Numerators as per given numbers 202/285, 405/120 is
GCF of Numerators i.e. for 202,405 is 1
LCM of denominators i.e. for 285,120 is 2280.
Thus, GCF of Fractions is 1/2280.Finally, GCF of Fractions for 202/285, 405/120 is 1/2280.