Use our free GCF of Fractions Calculator tool to compute the GCF of 21/374, 54/347, 290/678 i.e 1/43994742 easily. The following is the detailed procedure to determine the greatest common factor of fractions 21/374, 54/347, 290/678.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 21/374,54/347,290/678
To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by
GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators
In the fractions 21/374,54/347,290/678, numerators are 21,54,290
Denominators are 374,347,678
The GCF of 21,54,290 is 1 .
LCM of 374,347,678 is 43994742.
The greatest common factor of 21/374,54/347,290/678 = [GCF of 21,54,290]/[LCM of 374,347,678]= 1/43994742
Therefore, the GCF of 21/374,54/347,290/678 is 1/43994742.
To find the highest common factor of 21,54,290, we have to find the factors of both numbers and list the highest common factor.
The factors of 21 are 1, 3, 7, 21
The factors of 54 are 1, 2, 3, 6, 9, 18, 27, 54
The factors of 290 are 1, 2, 5, 10, 29, 58, 145, 290
The HCF of 21,54,290 is 1.
Lets's calculate GCF of 21,54,290
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 21
:1,3,7,21
Now, list down the factors of 54
:1,2,3,6,9,18,27,54
Now, list down the factors of 290
:1,2,5,10,29,58,145,290
Greatest Common Factor
We found the factors 21,54,290 . The biggest common factor number is the GCF number.
So the greatest common factor 21,54,290 is 1.
Lets's calculate LCM of 374,347,678
2 | 374, 347, 678 |
187, 347, 339 |
∴ So the LCM of the given numbers is 2 x 187 x 347 x 339 = 43994742
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/43994742
Therefore, the GCF of Fractions 21/374,54/347,290/678 is 1/43994742
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 374,347,678 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(374,347,678) = 1
common factors(in case of two or more numbers have common factors) = 2
GCF(374,347,678) x common factors =1 x 2 = 2
LCM(374,347,678) = ( 374 × 347 × 678 ) / 2
LCM(374,347,678) = 87989484 / 2
LCM(374,347,678) = 43994742
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 21,54,290?
The HCF of 21,54,290 is 1
2. What is the GCF of a fraction?
The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.
3. 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.
4. What is the GCF of Fractions for 21/374, 54/347, 290/678?
Answer: GCF of Numerators as per given numbers 21/374, 54/347, 290/678 is
GCF of Numerators i.e. for 21,54,290 is 1
LCM of denominators i.e. for 374,347,678 is 43994742.
Thus, GCF of Fractions is 1/43994742.Finally, GCF of Fractions for 21/374, 54/347, 290/678 is 1/43994742.