Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 278/13,512/49,278/33
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 278,512,278
Greatest Common Factor of Numerators i.e. GCF of 278,512,278 is 2 .
LCM of Denominators means LCM of 13,49,33 as per the given fractions.
LCM of 13,49,33 is 21021 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 278,512,278
2 | 278, 512, 278 |
139, 256, 139 |
∴ So the GCF of the given numbers is 2 = 2
Factors of 278
List of positive integer factors of 278 that divides 278 without a remainder.
1,2,139,278
Factors of 512
List of positive integer factors of 512 that divides 512 without a remainder.
1,2,4,8,16,32,64,128,256,512
Factors of 278
List of positive integer factors of 278 that divides 278 without a remainder.
1,2,139,278
Greatest Common Factor
We found the factors 278,512,278 . The biggest common factor number is the GCF number.
So the greatest common factor 278,512,278 is 2.
Lets's calculate LCM of 13,49,33
Given numbers has no common factors except 1. So, there LCM is their product i.e 21021
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/21021
Therefore, the GCF of Fractions 278/13,512/49,278/33 is 2/21021
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 13,49,33 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(13,49,33) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(13,49,33) x common factors =1 x 1 = 1
LCM(13,49,33) = ( 13 × 49 × 33 ) / 1
LCM(13,49,33) = 21021 / 1
LCM(13,49,33) = 21021
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 278/13, 512/49, 278/33?
Answer: GCF of Numerators as per given numbers 278/13, 512/49, 278/33 is
GCF of Numerators i.e. for 278,512,278 is 2
LCM of denominators i.e. for 13,49,33 is 21021.
Thus, GCF of Fractions is 2/21021.Finally, GCF of Fractions for 278/13, 512/49, 278/33 is 2/21021.