Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 9/42,574/30,749/66
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 9,574,749
Greatest Common Factor of Numerators i.e. GCF of 9,574,749 is 1 .
LCM of Denominators means LCM of 42,30,66 as per the given fractions.
LCM of 42,30,66 is 2310 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 9,574,749
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 9
List of positive integer factors of 9 that divides 9 without a remainder.
1,3,9
Factors of 574
List of positive integer factors of 574 that divides 574 without a remainder.
1,2,7,14,41,82,287,574
Factors of 749
List of positive integer factors of 749 that divides 749 without a remainder.
1,7,107,749
Greatest Common Factor
We found the factors 9,574,749 . The biggest common factor number is the GCF number.
So the greatest common factor 9,574,749 is 1.
Lets's calculate LCM of 42,30,66
2 | 42, 30, 66 |
3 | 21, 15, 33 |
7, 5, 11 |
∴ So the LCM of the given numbers is 2 x 3 x 7 x 5 x 11 = 2310
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2310
Therefore, the GCF of Fractions 9/42,574/30,749/66 is 1/2310
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 42,30,66 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(42,30,66) = 6
common factors(in case of two or more numbers have common factors) = 6
GCF(42,30,66) x common factors =6 x 6 = 36
LCM(42,30,66) = ( 42 × 30 × 66 ) / 36
LCM(42,30,66) = 83160 / 36
LCM(42,30,66) = 2310
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 9/42, 574/30, 749/66?
Answer: GCF of Numerators as per given numbers 9/42, 574/30, 749/66 is
GCF of Numerators i.e. for 9,574,749 is 1
LCM of denominators i.e. for 42,30,66 is 2310.
Thus, GCF of Fractions is 1/2310.Finally, GCF of Fractions for 9/42, 574/30, 749/66 is 1/2310.