Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 49/59,54/72,78/45,17/27
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 49,54,78,17
Greatest Common Factor of Numerators i.e. GCF of 49,54,78,17 is 1 .
LCM of Denominators means LCM of 59,72,45,27 as per the given fractions.
LCM of 59,72,45,27 is 63720 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 49,54,78,17
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 49
List of positive integer factors of 49 that divides 49 without a remainder.
1,7,49
Factors of 54
List of positive integer factors of 54 that divides 54 without a remainder.
1,2,3,6,9,18,27,54
Factors of 78
List of positive integer factors of 78 that divides 78 without a remainder.
1,2,3,6,13,26,39,78
Factors of 17
List of positive integer factors of 17 that divides 17 without a remainder.
1,17
Greatest Common Factor
We found the factors 49,54,78,17 . The biggest common factor number is the GCF number.
So the greatest common factor 49,54,78,17 is 1.
Lets's calculate LCM of 59,72,45,27
3 | 59, 72, 45, 27 |
3 | 59, 24, 15, 9 |
59, 8, 5, 3 |
∴ So the LCM of the given numbers is 3 x 3 x 59 x 8 x 5 x 3 = 63720
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/63720
Therefore, the GCF of Fractions 49/59,54/72,78/45,17/27 is 1/63720
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 59,72,45,27 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(59,72,45,27) = 1
common factors(in case of two or more numbers have common factors) = 81
GCF(59,72,45,27) x common factors =1 x 81 = 81
LCM(59,72,45,27) = ( 59 × 72 × 45 × 27 ) / 81
LCM(59,72,45,27) = 5161320 / 81
LCM(59,72,45,27) = 63720
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 49/59, 54/72, 78/45, 17/27?
Answer: GCF of Numerators as per given numbers 49/59, 54/72, 78/45, 17/27 is
GCF of Numerators i.e. for 49,54,78,17 is 1
LCM of denominators i.e. for 59,72,45,27 is 63720.
Thus, GCF of Fractions is 1/63720.Finally, GCF of Fractions for 49/59, 54/72, 78/45, 17/27 is 1/63720.