Use our free GCF of Fractions Calculator tool to compute the GCF of 92/57, 74/92, 61/69, 78/39 i.e 1/68172 easily. The following is the detailed procedure to determine the greatest common factor of fractions 92/57, 74/92, 61/69, 78/39.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 92/57,74/92,61/69,78/39
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 92/57,74/92,61/69,78/39, numerators are 92,74,61,78
Denominators are 57,92,69,39
The GCF of 92,74,61,78 is 1 .
LCM of 57,92,69,39 is 68172.
The greatest common factor of 92/57,74/92,61/69,78/39 = [GCF of 92,74,61,78]/[LCM of 57,92,69,39]= 1/68172
Therefore, the GCF of 92/57,74/92,61/69,78/39 is 1/68172.
To find the highest common factor of 92,74,61,78, we have to find the factors of both numbers and list the highest common factor.
The factors of 92 are 1, 2, 4, 23, 46, 92
The factors of 74 are 1, 2, 37, 74
The factors of 61 are 1, 61
The factors of 78 are 1, 2, 3, 6, 13, 26, 39, 78
The HCF of 92,74,61,78 is 1.
Lets's calculate GCF of 92,74,61,78
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 92
:1,2,4,23,46,92
Now, list down the factors of 74
:1,2,37,74
Now, list down the factors of 61
:1,61
Now, list down the factors of 78
:1,2,3,6,13,26,39,78
Greatest Common Factor
We found the factors 92,74,61,78 . The biggest common factor number is the GCF number.
So the greatest common factor 92,74,61,78 is 1.
Lets's calculate LCM of 57,92,69,39
3 | 57, 92, 69, 39 |
23 | 19, 92, 23, 13 |
19, 4, 1, 13 |
∴ So the LCM of the given numbers is 3 x 23 x 19 x 4 x 1 x 13 = 68172
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/68172
Therefore, the GCF of Fractions 92/57,74/92,61/69,78/39 is 1/68172
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 57,92,69,39 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(57,92,69,39) = 1
common factors(in case of two or more numbers have common factors) = 207
GCF(57,92,69,39) x common factors =1 x 207 = 207
LCM(57,92,69,39) = ( 57 × 92 × 69 × 39 ) / 207
LCM(57,92,69,39) = 14111604 / 207
LCM(57,92,69,39) = 68172
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 92,74,61,78?
The HCF of 92,74,61,78 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 92/57, 74/92, 61/69, 78/39?
Answer: GCF of Numerators as per given numbers 92/57, 74/92, 61/69, 78/39 is
GCF of Numerators i.e. for 92,74,61,78 is 1
LCM of denominators i.e. for 57,92,69,39 is 68172.
Thus, GCF of Fractions is 1/68172.Finally, GCF of Fractions for 92/57, 74/92, 61/69, 78/39 is 1/68172.