Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 34/60,14/84,14/15,14/347
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 34,14,14,14
Greatest Common Factor of Numerators i.e. GCF of 34,14,14,14 is 2 .
LCM of Denominators means LCM of 60,84,15,347 as per the given fractions.
LCM of 60,84,15,347 is 145740 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 34,14,14,14
2 | 34, 14, 14, 14 |
17, 7, 7, 7 |
∴ 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 14
List of positive integer factors of 14 that divides 14 without a remainder.
1,2,7,14
Factors of 14
List of positive integer factors of 14 that divides 14 without a remainder.
1,2,7,14
Factors of 14
List of positive integer factors of 14 that divides 14 without a remainder.
1,2,7,14
Greatest Common Factor
We found the factors 34,14,14,14 . The biggest common factor number is the GCF number.
So the greatest common factor 34,14,14,14 is 2.
Lets's calculate LCM of 60,84,15,347
2 | 60, 84, 15, 347 |
2 | 30, 42, 15, 347 |
3 | 15, 21, 15, 347 |
5 | 5, 7, 5, 347 |
1, 7, 1, 347 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 5 x 1 x 7 x 1 x 347 = 145740
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/145740
Therefore, the GCF of Fractions 34/60,14/84,14/15,14/347 is 2/145740
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 60,84,15,347 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(60,84,15,347) = 1
common factors(in case of two or more numbers have common factors) = 180
GCF(60,84,15,347) x common factors =1 x 180 = 180
LCM(60,84,15,347) = ( 60 × 84 × 15 × 347 ) / 180
LCM(60,84,15,347) = 26233200 / 180
LCM(60,84,15,347) = 145740
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 34/60, 14/84, 14/15, 14/347?
Answer: GCF of Numerators as per given numbers 34/60, 14/84, 14/15, 14/347 is
GCF of Numerators i.e. for 34,14,14,14 is 2
LCM of denominators i.e. for 60,84,15,347 is 145740.
Thus, GCF of Fractions is 2/145740.Finally, GCF of Fractions for 34/60, 14/84, 14/15, 14/347 is 2/145740.