GCF of 288/678, 128/427
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 288/678, 128/427 i.e 32/289506 easily. The following is the detailed procedure to determine the greatest common factor of fractions 288/678, 128/427.
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 288/678,128/427?
Given fractions are 288/678,128/427
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 288/678,128/427, numerators are 288,128
Denominators are 678,427
The GCF of 288,128 is 32 .
LCM of 678,427 is 289506.
The greatest common factor of 288/678,128/427 = [GCF of 288,128]/[LCM of 678,427]= 32/289506
Therefore, the GCF of 288/678,128/427 is 32/289506.
To find the highest common factor of 288,128, we have to find the factors of both numbers and list the highest common factor.
The factors of 288 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 288
The factors of 128 are 1, 2, 4, 8, 16, 32, 64, 128
The HCF of 288,128 is 32.
Lets's calculate GCF of 288,128
| 2 | 288, 128 |
| 2 | 144, 64 |
| 2 | 72, 32 |
| 2 | 36, 16 |
| 2 | 18, 8 |
| 9, 4 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 x 2 = 32
Greatest Common Factor of 288,128 By Matching Biggest Common Factor Method
Now, list down the factors of 288
:1,2,3,4,6,8,9,12,16,18,24,32,36,48,72,96,144,288
Now, list down the factors of 128
:1,2,4,8,16,32,64,128
Greatest Common Factor
We found the factors 288,128 . The biggest common factor number is the GCF number.
So the greatest common factor 288,128 is 32.
Lets's calculate LCM of 678,427
Given numbers has no common factors except 1. So, there LCM is their product i.e 289506
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 32/289506
Therefore, the GCF of Fractions 288/678,128/427 is 32/289506
Least Common Multiple of 678,427 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 678,427 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(678,427) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(678,427) x common factors =1 x 1 = 1
LCM(678,427) = ( 678 × 427 ) / 1
LCM(678,427) = 289506 / 1
LCM(678,427) = 289506
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 288/678, 128/427
1. What is the HCF of 288,128?
The HCF of 288,128 is 32
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 288/678, 128/427?
Answer: GCF of Numerators as per given numbers 288/678, 128/427 is
GCF of Numerators i.e. for 288,128 is 32
LCM of denominators i.e. for 678,427 is 289506.
Thus, GCF of Fractions is 32/289506.Finally, GCF of Fractions for 288/678, 128/427 is 32/289506.