GCF of 235/58, 282/2054
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 235/58, 282/2054 i.e 47/59566 easily. The following is the detailed procedure to determine the greatest common factor of fractions 235/58, 282/2054.
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 235/58,282/2054?
Given fractions are 235/58,282/2054
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 235/58,282/2054, numerators are 235,282
Denominators are 58,2054
The GCF of 235,282 is 47 .
LCM of 58,2054 is 59566.
The greatest common factor of 235/58,282/2054 = [GCF of 235,282]/[LCM of 58,2054]= 47/59566
Therefore, the GCF of 235/58,282/2054 is 47/59566.
To find the highest common factor of 235,282, we have to find the factors of both numbers and list the highest common factor.
The factors of 235 are 1, 5, 47, 235
The factors of 282 are 1, 2, 3, 6, 47, 94, 141, 282
The HCF of 235,282 is 47.
Lets's calculate GCF of 235,282
| 47 | 235, 282 |
| 5, 6 |
∴ So the GCF of the given numbers is 47 = 47
Greatest Common Factor of 235,282 By Matching Biggest Common Factor Method
Now, list down the factors of 235
:1,5,47,235
Now, list down the factors of 282
:1,2,3,6,47,94,141,282
Greatest Common Factor
We found the factors 235,282 . The biggest common factor number is the GCF number.
So the greatest common factor 235,282 is 47.
Lets's calculate LCM of 58,2054
| 2 | 58, 2054 |
| 29, 1027 |
∴ So the LCM of the given numbers is 2 x 29 x 1027 = 59566
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 47/59566
Therefore, the GCF of Fractions 235/58,282/2054 is 47/59566
Least Common Multiple of 58,2054 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 58,2054 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(58,2054) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(58,2054) x common factors =2 x 1 = 2
LCM(58,2054) = ( 58 × 2054 ) / 2
LCM(58,2054) = 119132 / 2
LCM(58,2054) = 59566
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FAQs on GCF of Fractions of 235/58, 282/2054
1. What is the HCF of 235,282?
The HCF of 235,282 is 47
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 235/58, 282/2054?
Answer: GCF of Numerators as per given numbers 235/58, 282/2054 is
GCF of Numerators i.e. for 235,282 is 47
LCM of denominators i.e. for 58,2054 is 59566.
Thus, GCF of Fractions is 47/59566.Finally, GCF of Fractions for 235/58, 282/2054 is 47/59566.