Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 74/16,36/90,42/39,740/23
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 74,36,42,740
Greatest Common Factor of Numerators i.e. GCF of 74,36,42,740 is 2 .
LCM of Denominators means LCM of 16,90,39,23 as per the given fractions.
LCM of 16,90,39,23 is 215280 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 74,36,42,740
2 | 74, 36, 42, 740 |
37, 18, 21, 370 |
∴ So the GCF of the given numbers is 2 = 2
Factors of 74
List of positive integer factors of 74 that divides 74 without a remainder.
1,2,37,74
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 42
List of positive integer factors of 42 that divides 42 without a remainder.
1,2,3,6,7,14,21,42
Factors of 740
List of positive integer factors of 740 that divides 740 without a remainder.
1,2,4,5,10,20,37,74,148,185,370,740
Greatest Common Factor
We found the factors 74,36,42,740 . The biggest common factor number is the GCF number.
So the greatest common factor 74,36,42,740 is 2.
Lets's calculate LCM of 16,90,39,23
2 | 16, 90, 39, 23 |
3 | 8, 45, 39, 23 |
8, 15, 13, 23 |
∴ So the LCM of the given numbers is 2 x 3 x 8 x 15 x 13 x 23 = 215280
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/215280
Therefore, the GCF of Fractions 74/16,36/90,42/39,740/23 is 2/215280
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 16,90,39,23 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(16,90,39,23) = 1
common factors(in case of two or more numbers have common factors) = 6
GCF(16,90,39,23) x common factors =1 x 6 = 6
LCM(16,90,39,23) = ( 16 × 90 × 39 × 23 ) / 6
LCM(16,90,39,23) = 1291680 / 6
LCM(16,90,39,23) = 215280
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 74/16, 36/90, 42/39, 740/23?
Answer: GCF of Numerators as per given numbers 74/16, 36/90, 42/39, 740/23 is
GCF of Numerators i.e. for 74,36,42,740 is 2
LCM of denominators i.e. for 16,90,39,23 is 215280.
Thus, GCF of Fractions is 2/215280.Finally, GCF of Fractions for 74/16, 36/90, 42/39, 740/23 is 2/215280.