Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 42/32,36/16,772/340
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 42,36,772
Greatest Common Factor of Numerators i.e. GCF of 42,36,772 is 2 .
LCM of Denominators means LCM of 32,16,340 as per the given fractions.
LCM of 32,16,340 is 2720 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 42,36,772
2 | 42, 36, 772 |
21, 18, 386 |
∴ So the GCF of the given numbers is 2 = 2
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 36
List of positive integer factors of 36 that divides 36 without a remainder.
1,2,3,4,6,9,12,18,36
Factors of 772
List of positive integer factors of 772 that divides 772 without a remainder.
1,2,4,193,386,772
Greatest Common Factor
We found the factors 42,36,772 . The biggest common factor number is the GCF number.
So the greatest common factor 42,36,772 is 2.
Lets's calculate LCM of 32,16,340
2 | 32, 16, 340 |
2 | 16, 8, 170 |
2 | 4, 8, 85 |
2 | 2, 4, 85 |
1, 2, 85 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 1 x 2 x 85 = 2720
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/2720
Therefore, the GCF of Fractions 42/32,36/16,772/340 is 2/2720
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 32,16,340 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(32,16,340) = 4
common factors(in case of two or more numbers have common factors) = 16
GCF(32,16,340) x common factors =4 x 16 = 64
LCM(32,16,340) = ( 32 × 16 × 340 ) / 64
LCM(32,16,340) = 174080 / 64
LCM(32,16,340) = 2720
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 42/32, 36/16, 772/340?
Answer: GCF of Numerators as per given numbers 42/32, 36/16, 772/340 is
GCF of Numerators i.e. for 42,36,772 is 2
LCM of denominators i.e. for 32,16,340 is 2720.
Thus, GCF of Fractions is 2/2720.Finally, GCF of Fractions for 42/32, 36/16, 772/340 is 2/2720.