Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 496/313,1322/414
Formula to find GCF of Fractions is
GCF = GCF of Numerators/LCM of Denominators
As per the formula GCF of Fractions let’s split into two parts and find the GCF of Numerators and LCM of Denominators
In the given fractions GCF of Numerators means GCF of 496,1322
Greatest Common Factor of Numerators i.e. GCF of 496,1322 is 2 .
LCM of Denominators means LCM of 313,414 as per the given fractions.
LCM of 313,414 is 129582 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 496,1322
2 | 496, 1322 |
248, 661 |
∴ So the GCF of the given numbers is 2 = 2
Factors of 496
List of positive integer factors of 496 that divides 496 without a remainder.
1,2,4,8,16,31,62,124,248,496
Factors of 1322
List of positive integer factors of 1322 that divides 1322 without a remainder.
1,2,661,1322
Greatest Common Factor
We found the factors 496,1322 . The biggest common factor number is the GCF number.
So the greatest common factor 496,1322 is 2.
Lets's calculate LCM of 313,414
Given numbers has no common factors except 1. So, there LCM is their product i.e 129582
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/129582
Therefore, the GCF of Fractions 496/313,1322/414 is 2/129582
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 313,414 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(313,414) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(313,414) x common factors =1 x 1 = 1
LCM(313,414) = ( 313 × 414 ) / 1
LCM(313,414) = 129582 / 1
LCM(313,414) = 129582
Here are some samples of GCF of Fractions calculations.
Here are some samples of GCF of Fractions calculations.
1. 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.
2. What is the GCF of Fractions for 496/313, 1322/414?
Answer: GCF of Numerators as per given numbers 496/313, 1322/414 is
GCF of Numerators i.e. for 496,1322 is 2
LCM of denominators i.e. for 313,414 is 129582.
Thus, GCF of Fractions is 2/129582.Finally, GCF of Fractions for 496/313, 1322/414 is 2/129582.