Use our free GCF of Fractions Calculator tool to compute the GCF of 256/553, 678/910 i.e 2/71890 easily. The following is the detailed procedure to determine the greatest common factor of fractions 256/553, 678/910.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 256/553,678/910
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 256/553,678/910, numerators are 256,678
Denominators are 553,910
The GCF of 256,678 is 2 .
LCM of 553,910 is 71890.
The greatest common factor of 256/553,678/910 = [GCF of 256,678]/[LCM of 553,910]= 2/71890
Therefore, the GCF of 256/553,678/910 is 2/71890.
To find the highest common factor of 256,678, we have to find the factors of both numbers and list the highest common factor.
The factors of 256 are 1, 2, 4, 8, 16, 32, 64, 128, 256
The factors of 678 are 1, 2, 3, 6, 113, 226, 339, 678
The HCF of 256,678 is 2.
Lets's calculate GCF of 256,678
2 | 256, 678 |
128, 339 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 256
:1,2,4,8,16,32,64,128,256
Now, list down the factors of 678
:1,2,3,6,113,226,339,678
Greatest Common Factor
We found the factors 256,678 . The biggest common factor number is the GCF number.
So the greatest common factor 256,678 is 2.
Lets's calculate LCM of 553,910
7 | 553, 910 |
79, 130 |
∴ So the LCM of the given numbers is 7 x 79 x 130 = 71890
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/71890
Therefore, the GCF of Fractions 256/553,678/910 is 2/71890
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 553,910 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(553,910) = 7
common factors(in case of two or more numbers have common factors) = 1
GCF(553,910) x common factors =7 x 1 = 7
LCM(553,910) = ( 553 × 910 ) / 7
LCM(553,910) = 503230 / 7
LCM(553,910) = 71890
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 256,678?
The HCF of 256,678 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 256/553, 678/910?
Answer: GCF of Numerators as per given numbers 256/553, 678/910 is
GCF of Numerators i.e. for 256,678 is 2
LCM of denominators i.e. for 553,910 is 71890.
Thus, GCF of Fractions is 2/71890.Finally, GCF of Fractions for 256/553, 678/910 is 2/71890.