Use our free GCF of Fractions Calculator tool to compute the GCF of 76/149, 52/409, 162/992 i.e 2/60453472 easily. The following is the detailed procedure to determine the greatest common factor of fractions 76/149, 52/409, 162/992.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 76/149,52/409,162/992
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 76/149,52/409,162/992, numerators are 76,52,162
Denominators are 149,409,992
The GCF of 76,52,162 is 2 .
LCM of 149,409,992 is 60453472.
The greatest common factor of 76/149,52/409,162/992 = [GCF of 76,52,162]/[LCM of 149,409,992]= 2/60453472
Therefore, the GCF of 76/149,52/409,162/992 is 2/60453472.
To find the highest common factor of 76,52,162, we have to find the factors of both numbers and list the highest common factor.
The factors of 76 are 1, 2, 4, 19, 38, 76
The factors of 52 are 1, 2, 4, 13, 26, 52
The factors of 162 are 1, 2, 3, 6, 9, 18, 27, 54, 81, 162
The HCF of 76,52,162 is 2.
Lets's calculate GCF of 76,52,162
2 | 76, 52, 162 |
38, 26, 81 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 76
:1,2,4,19,38,76
Now, list down the factors of 52
:1,2,4,13,26,52
Now, list down the factors of 162
:1,2,3,6,9,18,27,54,81,162
Greatest Common Factor
We found the factors 76,52,162 . The biggest common factor number is the GCF number.
So the greatest common factor 76,52,162 is 2.
Lets's calculate LCM of 149,409,992
Given numbers has no common factors except 1. So, there LCM is their product i.e 60453472
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/60453472
Therefore, the GCF of Fractions 76/149,52/409,162/992 is 2/60453472
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 149,409,992 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(149,409,992) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(149,409,992) x common factors =1 x 1 = 1
LCM(149,409,992) = ( 149 × 409 × 992 ) / 1
LCM(149,409,992) = 60453472 / 1
LCM(149,409,992) = 60453472
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 76,52,162?
The HCF of 76,52,162 is 2
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 76/149, 52/409, 162/992?
Answer: GCF of Numerators as per given numbers 76/149, 52/409, 162/992 is
GCF of Numerators i.e. for 76,52,162 is 2
LCM of denominators i.e. for 149,409,992 is 60453472.
Thus, GCF of Fractions is 2/60453472.Finally, GCF of Fractions for 76/149, 52/409, 162/992 is 2/60453472.