Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 82/42,32/10,565/300
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 82,32,565
Greatest Common Factor of Numerators i.e. GCF of 82,32,565 is 1 .
LCM of Denominators means LCM of 42,10,300 as per the given fractions.
LCM of 42,10,300 is 2100 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 82,32,565
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 82
List of positive integer factors of 82 that divides 82 without a remainder.
1,2,41,82
Factors of 32
List of positive integer factors of 32 that divides 32 without a remainder.
1,2,4,8,16,32
Factors of 565
List of positive integer factors of 565 that divides 565 without a remainder.
1,5,113,565
Greatest Common Factor
We found the factors 82,32,565 . The biggest common factor number is the GCF number.
So the greatest common factor 82,32,565 is 1.
Lets's calculate LCM of 42,10,300
2 | 42, 10, 300 |
3 | 21, 5, 150 |
5 | 7, 5, 50 |
7, 1, 10 |
∴ So the LCM of the given numbers is 2 x 3 x 5 x 7 x 1 x 10 = 2100
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2100
Therefore, the GCF of Fractions 82/42,32/10,565/300 is 1/2100
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 42,10,300 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(42,10,300) = 2
common factors(in case of two or more numbers have common factors) = 30
GCF(42,10,300) x common factors =2 x 30 = 60
LCM(42,10,300) = ( 42 × 10 × 300 ) / 60
LCM(42,10,300) = 126000 / 60
LCM(42,10,300) = 2100
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 82/42, 32/10, 565/300?
Answer: GCF of Numerators as per given numbers 82/42, 32/10, 565/300 is
GCF of Numerators i.e. for 82,32,565 is 1
LCM of denominators i.e. for 42,10,300 is 2100.
Thus, GCF of Fractions is 1/2100.Finally, GCF of Fractions for 82/42, 32/10, 565/300 is 1/2100.