Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 266/120,2800/152
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 266,2800
Greatest Common Factor of Numerators i.e. GCF of 266,2800 is 14 .
LCM of Denominators means LCM of 120,152 as per the given fractions.
LCM of 120,152 is 2280 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 266,2800
2 | 266, 2800 |
7 | 133, 1400 |
19, 200 |
∴ So the GCF of the given numbers is 2 x 7 = 14
Factors of 266
List of positive integer factors of 266 that divides 266 without a remainder.
1,2,7,14,19,38,133,266
Factors of 2800
List of positive integer factors of 2800 that divides 2800 without a remainder.
1,2,4,5,7,8,10,14,16,20,25,28,35,40,50,56,70,80,100,112,140,175,200,280,350,400,560,700,1400,2800
Greatest Common Factor
We found the factors 266,2800 . The biggest common factor number is the GCF number.
So the greatest common factor 266,2800 is 14.
Lets's calculate LCM of 120,152
2 | 120, 152 |
2 | 60, 76 |
2 | 30, 38 |
15, 19 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 15 x 19 = 2280
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/2280
Therefore, the GCF of Fractions 266/120,2800/152 is 14/2280
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 120,152 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(120,152) = 8
common factors(in case of two or more numbers have common factors) = 1
GCF(120,152) x common factors =8 x 1 = 8
LCM(120,152) = ( 120 × 152 ) / 8
LCM(120,152) = 18240 / 8
LCM(120,152) = 2280
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 266/120, 2800/152?
Answer: GCF of Numerators as per given numbers 266/120, 2800/152 is
GCF of Numerators i.e. for 266,2800 is 14
LCM of denominators i.e. for 120,152 is 2280.
Thus, GCF of Fractions is 14/2280.Finally, GCF of Fractions for 266/120, 2800/152 is 14/2280.