Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 32/205,78/107,616/384
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 32,78,616
Greatest Common Factor of Numerators i.e. GCF of 32,78,616 is 2 .
LCM of Denominators means LCM of 205,107,384 as per the given fractions.
LCM of 205,107,384 is 8423040 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 32,78,616
2 | 32, 78, 616 |
16, 39, 308 |
∴ So the GCF of the given numbers is 2 = 2
Factors of 32
List of positive integer factors of 32 that divides 32 without a remainder.
1,2,4,8,16,32
Factors of 78
List of positive integer factors of 78 that divides 78 without a remainder.
1,2,3,6,13,26,39,78
Factors of 616
List of positive integer factors of 616 that divides 616 without a remainder.
1,2,4,7,8,11,14,22,28,44,56,77,88,154,308,616
Greatest Common Factor
We found the factors 32,78,616 . The biggest common factor number is the GCF number.
So the greatest common factor 32,78,616 is 2.
Lets's calculate LCM of 205,107,384
Given numbers has no common factors except 1. So, there LCM is their product i.e 8423040
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/8423040
Therefore, the GCF of Fractions 32/205,78/107,616/384 is 2/8423040
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 205,107,384 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(205,107,384) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(205,107,384) x common factors =1 x 1 = 1
LCM(205,107,384) = ( 205 × 107 × 384 ) / 1
LCM(205,107,384) = 8423040 / 1
LCM(205,107,384) = 8423040
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 32/205, 78/107, 616/384?
Answer: GCF of Numerators as per given numbers 32/205, 78/107, 616/384 is
GCF of Numerators i.e. for 32,78,616 is 2
LCM of denominators i.e. for 205,107,384 is 8423040.
Thus, GCF of Fractions is 2/8423040.Finally, GCF of Fractions for 32/205, 78/107, 616/384 is 2/8423040.