Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 9/84,9/80,39/60,57/355
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 9,9,39,57
Greatest Common Factor of Numerators i.e. GCF of 9,9,39,57 is 3 .
LCM of Denominators means LCM of 84,80,60,355 as per the given fractions.
LCM of 84,80,60,355 is 119280 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 9,9,39,57
3 | 9, 9, 39, 57 |
3, 3, 13, 19 |
∴ So the GCF of the given numbers is 3 = 3
Factors of 9
List of positive integer factors of 9 that divides 9 without a remainder.
1,3,9
Factors of 9
List of positive integer factors of 9 that divides 9 without a remainder.
1,3,9
Factors of 39
List of positive integer factors of 39 that divides 39 without a remainder.
1,3,13,39
Factors of 57
List of positive integer factors of 57 that divides 57 without a remainder.
1,3,19,57
Greatest Common Factor
We found the factors 9,9,39,57 . The biggest common factor number is the GCF number.
So the greatest common factor 9,9,39,57 is 3.
Lets's calculate LCM of 84,80,60,355
2 | 84, 80, 60, 355 |
2 | 42, 40, 30, 355 |
3 | 21, 20, 15, 355 |
5 | 7, 20, 5, 355 |
7, 4, 1, 71 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 5 x 7 x 4 x 1 x 71 = 119280
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/119280
Therefore, the GCF of Fractions 9/84,9/80,39/60,57/355 is 3/119280
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 84,80,60,355 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(84,80,60,355) = 1
common factors(in case of two or more numbers have common factors) = 1200
GCF(84,80,60,355) x common factors =1 x 1200 = 1200
LCM(84,80,60,355) = ( 84 × 80 × 60 × 355 ) / 1200
LCM(84,80,60,355) = 143136000 / 1200
LCM(84,80,60,355) = 119280
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 9/84, 9/80, 39/60, 57/355?
Answer: GCF of Numerators as per given numbers 9/84, 9/80, 39/60, 57/355 is
GCF of Numerators i.e. for 9,9,39,57 is 3
LCM of denominators i.e. for 84,80,60,355 is 119280.
Thus, GCF of Fractions is 3/119280.Finally, GCF of Fractions for 9/84, 9/80, 39/60, 57/355 is 3/119280.