GCF of 28/71, 74/98, 256/189
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 28/71, 74/98, 256/189 i.e 2/187866 easily. The following is the detailed procedure to determine the greatest common factor of fractions 28/71, 74/98, 256/189.
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 28/71,74/98,256/189?
Given fractions are 28/71,74/98,256/189
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 28/71,74/98,256/189, numerators are 28,74,256
Denominators are 71,98,189
The GCF of 28,74,256 is 2 .
LCM of 71,98,189 is 187866.
The greatest common factor of 28/71,74/98,256/189 = [GCF of 28,74,256]/[LCM of 71,98,189]= 2/187866
Therefore, the GCF of 28/71,74/98,256/189 is 2/187866.
To find the highest common factor of 28,74,256, we have to find the factors of both numbers and list the highest common factor.
The factors of 28 are 1, 2, 4, 7, 14, 28
The factors of 74 are 1, 2, 37, 74
The factors of 256 are 1, 2, 4, 8, 16, 32, 64, 128, 256
The HCF of 28,74,256 is 2.
Lets's calculate GCF of 28,74,256
| 2 | 28, 74, 256 |
| 14, 37, 128 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 28,74,256 By Matching Biggest Common Factor Method
Now, list down the factors of 28
:1,2,4,7,14,28
Now, list down the factors of 74
:1,2,37,74
Now, list down the factors of 256
:1,2,4,8,16,32,64,128,256
Greatest Common Factor
We found the factors 28,74,256 . The biggest common factor number is the GCF number.
So the greatest common factor 28,74,256 is 2.
Lets's calculate LCM of 71,98,189
| 7 | 71, 98, 189 |
| 71, 14, 27 |
∴ So the LCM of the given numbers is 7 x 71 x 14 x 27 = 187866
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/187866
Therefore, the GCF of Fractions 28/71,74/98,256/189 is 2/187866
Least Common Multiple of 71,98,189 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 71,98,189 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(71,98,189) = 1
common factors(in case of two or more numbers have common factors) = 7
GCF(71,98,189) x common factors =1 x 7 = 7
LCM(71,98,189) = ( 71 × 98 × 189 ) / 7
LCM(71,98,189) = 1315062 / 7
LCM(71,98,189) = 187866
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 28/71, 74/98, 256/189
1. What is the HCF of 28,74,256?
The HCF of 28,74,256 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 28/71, 74/98, 256/189?
Answer: GCF of Numerators as per given numbers 28/71, 74/98, 256/189 is
GCF of Numerators i.e. for 28,74,256 is 2
LCM of denominators i.e. for 71,98,189 is 187866.
Thus, GCF of Fractions is 2/187866.Finally, GCF of Fractions for 28/71, 74/98, 256/189 is 2/187866.