Use our free GCF of Fractions Calculator tool to compute the GCF of 402/105, 442/775 i.e 2/16275 easily. The following is the detailed procedure to determine the greatest common factor of fractions 402/105, 442/775.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 402/105,442/775
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 402/105,442/775, numerators are 402,442
Denominators are 105,775
The GCF of 402,442 is 2 .
LCM of 105,775 is 16275.
The greatest common factor of 402/105,442/775 = [GCF of 402,442]/[LCM of 105,775]= 2/16275
Therefore, the GCF of 402/105,442/775 is 2/16275.
To find the highest common factor of 402,442, we have to find the factors of both numbers and list the highest common factor.
The factors of 402 are 1, 2, 3, 6, 67, 134, 201, 402
The factors of 442 are 1, 2, 13, 17, 26, 34, 221, 442
The HCF of 402,442 is 2.
Lets's calculate GCF of 402,442
2 | 402, 442 |
201, 221 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 402
:1,2,3,6,67,134,201,402
Now, list down the factors of 442
:1,2,13,17,26,34,221,442
Greatest Common Factor
We found the factors 402,442 . The biggest common factor number is the GCF number.
So the greatest common factor 402,442 is 2.
Lets's calculate LCM of 105,775
5 | 105, 775 |
21, 155 |
∴ So the LCM of the given numbers is 5 x 21 x 155 = 16275
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/16275
Therefore, the GCF of Fractions 402/105,442/775 is 2/16275
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 105,775 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(105,775) = 5
common factors(in case of two or more numbers have common factors) = 1
GCF(105,775) x common factors =5 x 1 = 5
LCM(105,775) = ( 105 × 775 ) / 5
LCM(105,775) = 81375 / 5
LCM(105,775) = 16275
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 402,442?
The HCF of 402,442 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 402/105, 442/775?
Answer: GCF of Numerators as per given numbers 402/105, 442/775 is
GCF of Numerators i.e. for 402,442 is 2
LCM of denominators i.e. for 105,775 is 16275.
Thus, GCF of Fractions is 2/16275.Finally, GCF of Fractions for 402/105, 442/775 is 2/16275.