Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 76/67,42/16,369/210
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 76,42,369
Greatest Common Factor of Numerators i.e. GCF of 76,42,369 is 1 .
LCM of Denominators means LCM of 67,16,210 as per the given fractions.
LCM of 67,16,210 is 112560 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 76,42,369
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 76
List of positive integer factors of 76 that divides 76 without a remainder.
1,2,4,19,38,76
Factors of 42
List of positive integer factors of 42 that divides 42 without a remainder.
1,2,3,6,7,14,21,42
Factors of 369
List of positive integer factors of 369 that divides 369 without a remainder.
1,3,9,41,123,369
Greatest Common Factor
We found the factors 76,42,369 . The biggest common factor number is the GCF number.
So the greatest common factor 76,42,369 is 1.
Lets's calculate LCM of 67,16,210
2 | 67, 16, 210 |
67, 8, 105 |
∴ So the LCM of the given numbers is 2 x 67 x 8 x 105 = 112560
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/112560
Therefore, the GCF of Fractions 76/67,42/16,369/210 is 1/112560
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 67,16,210 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(67,16,210) = 1
common factors(in case of two or more numbers have common factors) = 2
GCF(67,16,210) x common factors =1 x 2 = 2
LCM(67,16,210) = ( 67 × 16 × 210 ) / 2
LCM(67,16,210) = 225120 / 2
LCM(67,16,210) = 112560
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 76/67, 42/16, 369/210?
Answer: GCF of Numerators as per given numbers 76/67, 42/16, 369/210 is
GCF of Numerators i.e. for 76,42,369 is 1
LCM of denominators i.e. for 67,16,210 is 112560.
Thus, GCF of Fractions is 1/112560.Finally, GCF of Fractions for 76/67, 42/16, 369/210 is 1/112560.