Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 306/91,738/70,423/302
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 306,738,423
Greatest Common Factor of Numerators i.e. GCF of 306,738,423 is 9 .
LCM of Denominators means LCM of 91,70,302 as per the given fractions.
LCM of 91,70,302 is 137410 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 306,738,423
3 | 306, 738, 423 |
3 | 102, 246, 141 |
34, 82, 47 |
∴ So the GCF of the given numbers is 3 x 3 = 9
Factors of 306
List of positive integer factors of 306 that divides 306 without a remainder.
1,2,3,6,9,17,18,34,51,102,153,306
Factors of 738
List of positive integer factors of 738 that divides 738 without a remainder.
1,2,3,6,9,18,41,82,123,246,369,738
Factors of 423
List of positive integer factors of 423 that divides 423 without a remainder.
1,3,9,47,141,423
Greatest Common Factor
We found the factors 306,738,423 . The biggest common factor number is the GCF number.
So the greatest common factor 306,738,423 is 9.
Lets's calculate LCM of 91,70,302
2 | 91, 70, 302 |
7 | 91, 35, 151 |
13, 5, 151 |
∴ So the LCM of the given numbers is 2 x 7 x 13 x 5 x 151 = 137410
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 9/137410
Therefore, the GCF of Fractions 306/91,738/70,423/302 is 9/137410
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 91,70,302 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(91,70,302) = 1
common factors(in case of two or more numbers have common factors) = 14
GCF(91,70,302) x common factors =1 x 14 = 14
LCM(91,70,302) = ( 91 × 70 × 302 ) / 14
LCM(91,70,302) = 1923740 / 14
LCM(91,70,302) = 137410
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 306/91, 738/70, 423/302?
Answer: GCF of Numerators as per given numbers 306/91, 738/70, 423/302 is
GCF of Numerators i.e. for 306,738,423 is 9
LCM of denominators i.e. for 91,70,302 is 137410.
Thus, GCF of Fractions is 9/137410.Finally, GCF of Fractions for 306/91, 738/70, 423/302 is 9/137410.