Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 65/23,45/68,49/76,41/76
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 65,45,49,41
Greatest Common Factor of Numerators i.e. GCF of 65,45,49,41 is 1 .
LCM of Denominators means LCM of 23,68,76,76 as per the given fractions.
LCM of 23,68,76,76 is 29716 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 65,45,49,41
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 65
List of positive integer factors of 65 that divides 65 without a remainder.
1,5,13,65
Factors of 45
List of positive integer factors of 45 that divides 45 without a remainder.
1,3,5,9,15,45
Factors of 49
List of positive integer factors of 49 that divides 49 without a remainder.
1,7,49
Factors of 41
List of positive integer factors of 41 that divides 41 without a remainder.
1,41
Greatest Common Factor
We found the factors 65,45,49,41 . The biggest common factor number is the GCF number.
So the greatest common factor 65,45,49,41 is 1.
Lets's calculate LCM of 23,68,76,76
2 | 23, 68, 76, 76 |
2 | 23, 34, 38, 38 |
19 | 23, 17, 19, 19 |
23, 17, 1, 1 |
∴ So the LCM of the given numbers is 2 x 2 x 19 x 23 x 17 x 1 x 1 = 29716
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/29716
Therefore, the GCF of Fractions 65/23,45/68,49/76,41/76 is 1/29716
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 23,68,76,76 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(23,68,76,76) = 1
common factors(in case of two or more numbers have common factors) = 304
GCF(23,68,76,76) x common factors =1 x 304 = 304
LCM(23,68,76,76) = ( 23 × 68 × 76 × 76 ) / 304
LCM(23,68,76,76) = 9033664 / 304
LCM(23,68,76,76) = 29716
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 65/23, 45/68, 49/76, 41/76?
Answer: GCF of Numerators as per given numbers 65/23, 45/68, 49/76, 41/76 is
GCF of Numerators i.e. for 65,45,49,41 is 1
LCM of denominators i.e. for 23,68,76,76 is 29716.
Thus, GCF of Fractions is 1/29716.Finally, GCF of Fractions for 65/23, 45/68, 49/76, 41/76 is 1/29716.