Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 42/49,37/96,20/80,69/35
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 42,37,20,69
Greatest Common Factor of Numerators i.e. GCF of 42,37,20,69 is 1 .
LCM of Denominators means LCM of 49,96,80,35 as per the given fractions.
LCM of 49,96,80,35 is 23520 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 42,37,20,69
∴ So GCF of numbers is 1 because of no common factors present between them.
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 37
List of positive integer factors of 37 that divides 37 without a remainder.
1,37
Factors of 20
List of positive integer factors of 20 that divides 20 without a remainder.
1,2,4,5,10,20
Factors of 69
List of positive integer factors of 69 that divides 69 without a remainder.
1,3,23,69
Greatest Common Factor
We found the factors 42,37,20,69 . The biggest common factor number is the GCF number.
So the greatest common factor 42,37,20,69 is 1.
Lets's calculate LCM of 49,96,80,35
2 | 49, 96, 80, 35 |
2 | 49, 48, 40, 35 |
2 | 49, 24, 20, 35 |
2 | 49, 12, 10, 35 |
5 | 49, 6, 5, 35 |
7 | 49, 6, 1, 7 |
1, 6, 1, 7 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 5 x 7 x 1 x 6 x 1 x 7 = 23520
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/23520
Therefore, the GCF of Fractions 42/49,37/96,20/80,69/35 is 1/23520
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 49,96,80,35 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(49,96,80,35) = 1
common factors(in case of two or more numbers have common factors) = 560
GCF(49,96,80,35) x common factors =1 x 560 = 560
LCM(49,96,80,35) = ( 49 × 96 × 80 × 35 ) / 560
LCM(49,96,80,35) = 13171200 / 560
LCM(49,96,80,35) = 23520
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 42/49, 37/96, 20/80, 69/35?
Answer: GCF of Numerators as per given numbers 42/49, 37/96, 20/80, 69/35 is
GCF of Numerators i.e. for 42,37,20,69 is 1
LCM of denominators i.e. for 49,96,80,35 is 23520.
Thus, GCF of Fractions is 1/23520.Finally, GCF of Fractions for 42/49, 37/96, 20/80, 69/35 is 1/23520.