Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 434/26,304/14,748/34
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 434,304,748
Greatest Common Factor of Numerators i.e. GCF of 434,304,748 is 2 .
LCM of Denominators means LCM of 26,14,34 as per the given fractions.
LCM of 26,14,34 is 3094 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 434,304,748
2 | 434, 304, 748 |
217, 152, 374 |
∴ So the GCF of the given numbers is 2 = 2
Factors of 434
List of positive integer factors of 434 that divides 434 without a remainder.
1,2,7,14,31,62,217,434
Factors of 304
List of positive integer factors of 304 that divides 304 without a remainder.
1,2,4,8,16,19,38,76,152,304
Factors of 748
List of positive integer factors of 748 that divides 748 without a remainder.
1,2,4,11,17,22,34,44,68,187,374,748
Greatest Common Factor
We found the factors 434,304,748 . The biggest common factor number is the GCF number.
So the greatest common factor 434,304,748 is 2.
Lets's calculate LCM of 26,14,34
2 | 26, 14, 34 |
13, 7, 17 |
∴ So the LCM of the given numbers is 2 x 13 x 7 x 17 = 3094
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/3094
Therefore, the GCF of Fractions 434/26,304/14,748/34 is 2/3094
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 26,14,34 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(26,14,34) = 2
common factors(in case of two or more numbers have common factors) = 2
GCF(26,14,34) x common factors =2 x 2 = 4
LCM(26,14,34) = ( 26 × 14 × 34 ) / 4
LCM(26,14,34) = 12376 / 4
LCM(26,14,34) = 3094
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 434/26, 304/14, 748/34?
Answer: GCF of Numerators as per given numbers 434/26, 304/14, 748/34 is
GCF of Numerators i.e. for 434,304,748 is 2
LCM of denominators i.e. for 26,14,34 is 3094.
Thus, GCF of Fractions is 2/3094.Finally, GCF of Fractions for 434/26, 304/14, 748/34 is 2/3094.