Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 54/28,438/65,282/178
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 54,438,282
Greatest Common Factor of Numerators i.e. GCF of 54,438,282 is 6 .
LCM of Denominators means LCM of 28,65,178 as per the given fractions.
LCM of 28,65,178 is 161980 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 54,438,282
2 | 54, 438, 282 |
3 | 27, 219, 141 |
9, 73, 47 |
∴ So the GCF of the given numbers is 2 x 3 = 6
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 438
List of positive integer factors of 438 that divides 438 without a remainder.
1,2,3,6,73,146,219,438
Factors of 282
List of positive integer factors of 282 that divides 282 without a remainder.
1,2,3,6,47,94,141,282
Greatest Common Factor
We found the factors 54,438,282 . The biggest common factor number is the GCF number.
So the greatest common factor 54,438,282 is 6.
Lets's calculate LCM of 28,65,178
2 | 28, 65, 178 |
14, 65, 89 |
∴ So the LCM of the given numbers is 2 x 14 x 65 x 89 = 161980
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/161980
Therefore, the GCF of Fractions 54/28,438/65,282/178 is 6/161980
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 28,65,178 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(28,65,178) = 1
common factors(in case of two or more numbers have common factors) = 2
GCF(28,65,178) x common factors =1 x 2 = 2
LCM(28,65,178) = ( 28 × 65 × 178 ) / 2
LCM(28,65,178) = 323960 / 2
LCM(28,65,178) = 161980
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 54/28, 438/65, 282/178?
Answer: GCF of Numerators as per given numbers 54/28, 438/65, 282/178 is
GCF of Numerators i.e. for 54,438,282 is 6
LCM of denominators i.e. for 28,65,178 is 161980.
Thus, GCF of Fractions is 6/161980.Finally, GCF of Fractions for 54/28, 438/65, 282/178 is 6/161980.