Use our free GCF of Fractions Calculator tool to compute the GCF of 58/506, 38/308, 166/406 i.e 2/205436 easily. The following is the detailed procedure to determine the greatest common factor of fractions 58/506, 38/308, 166/406.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 58/506,38/308,166/406
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 58/506,38/308,166/406, numerators are 58,38,166
Denominators are 506,308,406
The GCF of 58,38,166 is 2 .
LCM of 506,308,406 is 205436.
The greatest common factor of 58/506,38/308,166/406 = [GCF of 58,38,166]/[LCM of 506,308,406]= 2/205436
Therefore, the GCF of 58/506,38/308,166/406 is 2/205436.
To find the highest common factor of 58,38,166, we have to find the factors of both numbers and list the highest common factor.
The factors of 58 are 1, 2, 29, 58
The factors of 38 are 1, 2, 19, 38
The factors of 166 are 1, 2, 83, 166
The HCF of 58,38,166 is 2.
Lets's calculate GCF of 58,38,166
2 | 58, 38, 166 |
29, 19, 83 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 58
:1,2,29,58
Now, list down the factors of 38
:1,2,19,38
Now, list down the factors of 166
:1,2,83,166
Greatest Common Factor
We found the factors 58,38,166 . The biggest common factor number is the GCF number.
So the greatest common factor 58,38,166 is 2.
Lets's calculate LCM of 506,308,406
2 | 506, 308, 406 |
7 | 253, 154, 203 |
11 | 253, 22, 29 |
23, 2, 29 |
∴ So the LCM of the given numbers is 2 x 7 x 11 x 23 x 2 x 29 = 205436
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/205436
Therefore, the GCF of Fractions 58/506,38/308,166/406 is 2/205436
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 506,308,406 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(506,308,406) = 2
common factors(in case of two or more numbers have common factors) = 154
GCF(506,308,406) x common factors =2 x 154 = 308
LCM(506,308,406) = ( 506 × 308 × 406 ) / 308
LCM(506,308,406) = 63274288 / 308
LCM(506,308,406) = 205436
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 58,38,166?
The HCF of 58,38,166 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 58/506, 38/308, 166/406?
Answer: GCF of Numerators as per given numbers 58/506, 38/308, 166/406 is
GCF of Numerators i.e. for 58,38,166 is 2
LCM of denominators i.e. for 506,308,406 is 205436.
Thus, GCF of Fractions is 2/205436.Finally, GCF of Fractions for 58/506, 38/308, 166/406 is 2/205436.