Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 24/73,30/73,65/15,84/16
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 24,30,65,84
Greatest Common Factor of Numerators i.e. GCF of 24,30,65,84 is 1 .
LCM of Denominators means LCM of 73,73,15,16 as per the given fractions.
LCM of 73,73,15,16 is 17520 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 24,30,65,84
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 24
List of positive integer factors of 24 that divides 24 without a remainder.
1,2,3,4,6,8,12,24
Factors of 30
List of positive integer factors of 30 that divides 30 without a remainder.
1,2,3,5,6,10,15,30
Factors of 65
List of positive integer factors of 65 that divides 65 without a remainder.
1,5,13,65
Factors of 84
List of positive integer factors of 84 that divides 84 without a remainder.
1,2,3,4,6,7,12,14,21,28,42,84
Greatest Common Factor
We found the factors 24,30,65,84 . The biggest common factor number is the GCF number.
So the greatest common factor 24,30,65,84 is 1.
Lets's calculate LCM of 73,73,15,16
73 | 73, 73, 15, 16 |
1, 1, 15, 16 |
∴ So the LCM of the given numbers is 73 x 1 x 1 x 15 x 16 = 17520
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/17520
Therefore, the GCF of Fractions 24/73,30/73,65/15,84/16 is 1/17520
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 73,73,15,16 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(73,73,15,16) = 1
common factors(in case of two or more numbers have common factors) = 73
GCF(73,73,15,16) x common factors =1 x 73 = 73
LCM(73,73,15,16) = ( 73 × 73 × 15 × 16 ) / 73
LCM(73,73,15,16) = 1278960 / 73
LCM(73,73,15,16) = 17520
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 24/73, 30/73, 65/15, 84/16?
Answer: GCF of Numerators as per given numbers 24/73, 30/73, 65/15, 84/16 is
GCF of Numerators i.e. for 24,30,65,84 is 1
LCM of denominators i.e. for 73,73,15,16 is 17520.
Thus, GCF of Fractions is 1/17520.Finally, GCF of Fractions for 24/73, 30/73, 65/15, 84/16 is 1/17520.