Use our free GCF of Fractions Calculator tool to compute the GCF of 42/78, 14/74, 695/54 i.e 1/25974 easily. The following is the detailed procedure to determine the greatest common factor of fractions 42/78, 14/74, 695/54.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 42/78,14/74,695/54
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 42/78,14/74,695/54, numerators are 42,14,695
Denominators are 78,74,54
The GCF of 42,14,695 is 1 .
LCM of 78,74,54 is 25974.
The greatest common factor of 42/78,14/74,695/54 = [GCF of 42,14,695]/[LCM of 78,74,54]= 1/25974
Therefore, the GCF of 42/78,14/74,695/54 is 1/25974.
To find the highest common factor of 42,14,695, we have to find the factors of both numbers and list the highest common factor.
The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42
The factors of 14 are 1, 2, 7, 14
The factors of 695 are 1, 5, 139, 695
The HCF of 42,14,695 is 1.
Lets's calculate GCF of 42,14,695
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 42
:1,2,3,6,7,14,21,42
Now, list down the factors of 14
:1,2,7,14
Now, list down the factors of 695
:1,5,139,695
Greatest Common Factor
We found the factors 42,14,695 . The biggest common factor number is the GCF number.
So the greatest common factor 42,14,695 is 1.
Lets's calculate LCM of 78,74,54
2 | 78, 74, 54 |
3 | 39, 37, 27 |
13, 37, 9 |
∴ So the LCM of the given numbers is 2 x 3 x 13 x 37 x 9 = 25974
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/25974
Therefore, the GCF of Fractions 42/78,14/74,695/54 is 1/25974
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 78,74,54 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(78,74,54) = 2
common factors(in case of two or more numbers have common factors) = 6
GCF(78,74,54) x common factors =2 x 6 = 12
LCM(78,74,54) = ( 78 × 74 × 54 ) / 12
LCM(78,74,54) = 311688 / 12
LCM(78,74,54) = 25974
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 42,14,695?
The HCF of 42,14,695 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 42/78, 14/74, 695/54?
Answer: GCF of Numerators as per given numbers 42/78, 14/74, 695/54 is
GCF of Numerators i.e. for 42,14,695 is 1
LCM of denominators i.e. for 78,74,54 is 25974.
Thus, GCF of Fractions is 1/25974.Finally, GCF of Fractions for 42/78, 14/74, 695/54 is 1/25974.