Use our free GCF of Fractions Calculator tool to compute the GCF of 7/67, 12/75, 58/404, 644/168 i.e 1/28421400 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7/67, 12/75, 58/404, 644/168.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 7/67,12/75,58/404,644/168
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 7/67,12/75,58/404,644/168, numerators are 7,12,58,644
Denominators are 67,75,404,168
The GCF of 7,12,58,644 is 1 .
LCM of 67,75,404,168 is 28421400.
The greatest common factor of 7/67,12/75,58/404,644/168 = [GCF of 7,12,58,644]/[LCM of 67,75,404,168]= 1/28421400
Therefore, the GCF of 7/67,12/75,58/404,644/168 is 1/28421400.
To find the highest common factor of 7,12,58,644, we have to find the factors of both numbers and list the highest common factor.
The factors of 7 are 1, 7
The factors of 12 are 1, 2, 3, 4, 6, 12
The factors of 58 are 1, 2, 29, 58
The factors of 644 are 1, 2, 4, 7, 14, 23, 28, 46, 92, 161, 322, 644
The HCF of 7,12,58,644 is 1.
Lets's calculate GCF of 7,12,58,644
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 7
:1,7
Now, list down the factors of 12
:1,2,3,4,6,12
Now, list down the factors of 58
:1,2,29,58
Now, list down the factors of 644
:1,2,4,7,14,23,28,46,92,161,322,644
Greatest Common Factor
We found the factors 7,12,58,644 . The biggest common factor number is the GCF number.
So the greatest common factor 7,12,58,644 is 1.
Lets's calculate LCM of 67,75,404,168
2 | 67, 75, 404, 168 |
2 | 67, 75, 202, 84 |
3 | 67, 75, 101, 42 |
67, 25, 101, 14 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 67 x 25 x 101 x 14 = 28421400
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/28421400
Therefore, the GCF of Fractions 7/67,12/75,58/404,644/168 is 1/28421400
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 67,75,404,168 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(67,75,404,168) = 1
common factors(in case of two or more numbers have common factors) = 12
GCF(67,75,404,168) x common factors =1 x 12 = 12
LCM(67,75,404,168) = ( 67 × 75 × 404 × 168 ) / 12
LCM(67,75,404,168) = 341056800 / 12
LCM(67,75,404,168) = 28421400
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 7,12,58,644?
The HCF of 7,12,58,644 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 7/67, 12/75, 58/404, 644/168?
Answer: GCF of Numerators as per given numbers 7/67, 12/75, 58/404, 644/168 is
GCF of Numerators i.e. for 7,12,58,644 is 1
LCM of denominators i.e. for 67,75,404,168 is 28421400.
Thus, GCF of Fractions is 1/28421400.Finally, GCF of Fractions for 7/67, 12/75, 58/404, 644/168 is 1/28421400.