Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 3/24,16/42,86/57,78/24
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 3,16,86,78
Greatest Common Factor of Numerators i.e. GCF of 3,16,86,78 is 1 .
LCM of Denominators means LCM of 24,42,57,24 as per the given fractions.
LCM of 24,42,57,24 is 3192 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 3,16,86,78
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 3
List of positive integer factors of 3 that divides 3 without a remainder.
1,3
Factors of 16
List of positive integer factors of 16 that divides 16 without a remainder.
1,2,4,8,16
Factors of 86
List of positive integer factors of 86 that divides 86 without a remainder.
1,2,43,86
Factors of 78
List of positive integer factors of 78 that divides 78 without a remainder.
1,2,3,6,13,26,39,78
Greatest Common Factor
We found the factors 3,16,86,78 . The biggest common factor number is the GCF number.
So the greatest common factor 3,16,86,78 is 1.
Lets's calculate LCM of 24,42,57,24
2 | 24, 42, 57, 24 |
2 | 12, 21, 57, 12 |
2 | 6, 21, 57, 6 |
3 | 3, 21, 57, 3 |
1, 7, 19, 1 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 3 x 1 x 7 x 19 x 1 = 3192
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/3192
Therefore, the GCF of Fractions 3/24,16/42,86/57,78/24 is 1/3192
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 24,42,57,24 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(24,42,57,24) = 3
common factors(in case of two or more numbers have common factors) = 144
GCF(24,42,57,24) x common factors =3 x 144 = 432
LCM(24,42,57,24) = ( 24 × 42 × 57 × 24 ) / 432
LCM(24,42,57,24) = 1378944 / 432
LCM(24,42,57,24) = 3192
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 3/24, 16/42, 86/57, 78/24?
Answer: GCF of Numerators as per given numbers 3/24, 16/42, 86/57, 78/24 is
GCF of Numerators i.e. for 3,16,86,78 is 1
LCM of denominators i.e. for 24,42,57,24 is 3192.
Thus, GCF of Fractions is 1/3192.Finally, GCF of Fractions for 3/24, 16/42, 86/57, 78/24 is 1/3192.