Use our free GCF of Fractions Calculator tool to compute the GCF of 430/253, 228/308 i.e 2/7084 easily. The following is the detailed procedure to determine the greatest common factor of fractions 430/253, 228/308.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 430/253,228/308
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 430/253,228/308, numerators are 430,228
Denominators are 253,308
The GCF of 430,228 is 2 .
LCM of 253,308 is 7084.
The greatest common factor of 430/253,228/308 = [GCF of 430,228]/[LCM of 253,308]= 2/7084
Therefore, the GCF of 430/253,228/308 is 2/7084.
To find the highest common factor of 430,228, we have to find the factors of both numbers and list the highest common factor.
The factors of 430 are 1, 2, 5, 10, 43, 86, 215, 430
The factors of 228 are 1, 2, 3, 4, 6, 12, 19, 38, 57, 76, 114, 228
The HCF of 430,228 is 2.
Lets's calculate GCF of 430,228
2 | 430, 228 |
215, 114 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 430
:1,2,5,10,43,86,215,430
Now, list down the factors of 228
:1,2,3,4,6,12,19,38,57,76,114,228
Greatest Common Factor
We found the factors 430,228 . The biggest common factor number is the GCF number.
So the greatest common factor 430,228 is 2.
Lets's calculate LCM of 253,308
11 | 253, 308 |
23, 28 |
∴ So the LCM of the given numbers is 11 x 23 x 28 = 7084
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/7084
Therefore, the GCF of Fractions 430/253,228/308 is 2/7084
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 253,308 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(253,308) = 11
common factors(in case of two or more numbers have common factors) = 1
GCF(253,308) x common factors =11 x 1 = 11
LCM(253,308) = ( 253 × 308 ) / 11
LCM(253,308) = 77924 / 11
LCM(253,308) = 7084
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 430,228?
The HCF of 430,228 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 430/253, 228/308?
Answer: GCF of Numerators as per given numbers 430/253, 228/308 is
GCF of Numerators i.e. for 430,228 is 2
LCM of denominators i.e. for 253,308 is 7084.
Thus, GCF of Fractions is 2/7084.Finally, GCF of Fractions for 430/253, 228/308 is 2/7084.