Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 165/24,549/14,113/49
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 165,549,113
Greatest Common Factor of Numerators i.e. GCF of 165,549,113 is 1 .
LCM of Denominators means LCM of 24,14,49 as per the given fractions.
LCM of 24,14,49 is 1176 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 165,549,113
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 165
List of positive integer factors of 165 that divides 165 without a remainder.
1,3,5,11,15,33,55,165
Factors of 549
List of positive integer factors of 549 that divides 549 without a remainder.
1,3,9,61,183,549
Factors of 113
List of positive integer factors of 113 that divides 113 without a remainder.
1,113
Greatest Common Factor
We found the factors 165,549,113 . The biggest common factor number is the GCF number.
So the greatest common factor 165,549,113 is 1.
Lets's calculate LCM of 24,14,49
2 | 24, 14, 49 |
7 | 12, 7, 49 |
12, 1, 7 |
∴ So the LCM of the given numbers is 2 x 7 x 12 x 1 x 7 = 1176
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1176
Therefore, the GCF of Fractions 165/24,549/14,113/49 is 1/1176
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 24,14,49 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(24,14,49) = 1
common factors(in case of two or more numbers have common factors) = 14
GCF(24,14,49) x common factors =1 x 14 = 14
LCM(24,14,49) = ( 24 × 14 × 49 ) / 14
LCM(24,14,49) = 16464 / 14
LCM(24,14,49) = 1176
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 165/24, 549/14, 113/49?
Answer: GCF of Numerators as per given numbers 165/24, 549/14, 113/49 is
GCF of Numerators i.e. for 165,549,113 is 1
LCM of denominators i.e. for 24,14,49 is 1176.
Thus, GCF of Fractions is 1/1176.Finally, GCF of Fractions for 165/24, 549/14, 113/49 is 1/1176.