Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 34/83,12/45,28/62,80/137
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 34,12,28,80
Greatest Common Factor of Numerators i.e. GCF of 34,12,28,80 is 2 .
LCM of Denominators means LCM of 83,45,62,137 as per the given fractions.
LCM of 83,45,62,137 is 31725090 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 34,12,28,80
2 | 34, 12, 28, 80 |
17, 6, 14, 40 |
∴ So the GCF of the given numbers is 2 = 2
Factors of 34
List of positive integer factors of 34 that divides 34 without a remainder.
1,2,17,34
Factors of 12
List of positive integer factors of 12 that divides 12 without a remainder.
1,2,3,4,6,12
Factors of 28
List of positive integer factors of 28 that divides 28 without a remainder.
1,2,4,7,14,28
Factors of 80
List of positive integer factors of 80 that divides 80 without a remainder.
1,2,4,5,8,10,16,20,40,80
Greatest Common Factor
We found the factors 34,12,28,80 . The biggest common factor number is the GCF number.
So the greatest common factor 34,12,28,80 is 2.
Lets's calculate LCM of 83,45,62,137
Given numbers has no common factors except 1. So, there LCM is their product i.e 31725090
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/31725090
Therefore, the GCF of Fractions 34/83,12/45,28/62,80/137 is 2/31725090
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 83,45,62,137 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(83,45,62,137) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(83,45,62,137) x common factors =1 x 1 = 1
LCM(83,45,62,137) = ( 83 × 45 × 62 × 137 ) / 1
LCM(83,45,62,137) = 31725090 / 1
LCM(83,45,62,137) = 31725090
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 34/83, 12/45, 28/62, 80/137?
Answer: GCF of Numerators as per given numbers 34/83, 12/45, 28/62, 80/137 is
GCF of Numerators i.e. for 34,12,28,80 is 2
LCM of denominators i.e. for 83,45,62,137 is 31725090.
Thus, GCF of Fractions is 2/31725090.Finally, GCF of Fractions for 34/83, 12/45, 28/62, 80/137 is 2/31725090.