Use our free GCF of Fractions Calculator tool to compute the GCF of 77/315, 747/522, 123/416 i.e 1/3800160 easily. The following is the detailed procedure to determine the greatest common factor of fractions 77/315, 747/522, 123/416.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 77/315,747/522,123/416
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 77/315,747/522,123/416, numerators are 77,747,123
Denominators are 315,522,416
The GCF of 77,747,123 is 1 .
LCM of 315,522,416 is 3800160.
The greatest common factor of 77/315,747/522,123/416 = [GCF of 77,747,123]/[LCM of 315,522,416]= 1/3800160
Therefore, the GCF of 77/315,747/522,123/416 is 1/3800160.
To find the highest common factor of 77,747,123, we have to find the factors of both numbers and list the highest common factor.
The factors of 77 are 1, 7, 11, 77
The factors of 747 are 1, 3, 9, 83, 249, 747
The factors of 123 are 1, 3, 41, 123
The HCF of 77,747,123 is 1.
Lets's calculate GCF of 77,747,123
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 77
:1,7,11,77
Now, list down the factors of 747
:1,3,9,83,249,747
Now, list down the factors of 123
:1,3,41,123
Greatest Common Factor
We found the factors 77,747,123 . The biggest common factor number is the GCF number.
So the greatest common factor 77,747,123 is 1.
Lets's calculate LCM of 315,522,416
2 | 315, 522, 416 |
3 | 315, 261, 208 |
3 | 105, 87, 208 |
35, 29, 208 |
∴ So the LCM of the given numbers is 2 x 3 x 3 x 35 x 29 x 208 = 3800160
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/3800160
Therefore, the GCF of Fractions 77/315,747/522,123/416 is 1/3800160
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 315,522,416 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(315,522,416) = 1
common factors(in case of two or more numbers have common factors) = 18
GCF(315,522,416) x common factors =1 x 18 = 18
LCM(315,522,416) = ( 315 × 522 × 416 ) / 18
LCM(315,522,416) = 68402880 / 18
LCM(315,522,416) = 3800160
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 77,747,123?
The HCF of 77,747,123 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 77/315, 747/522, 123/416?
Answer: GCF of Numerators as per given numbers 77/315, 747/522, 123/416 is
GCF of Numerators i.e. for 77,747,123 is 1
LCM of denominators i.e. for 315,522,416 is 3800160.
Thus, GCF of Fractions is 1/3800160.Finally, GCF of Fractions for 77/315, 747/522, 123/416 is 1/3800160.