Use our free GCF of Fractions Calculator tool to compute the GCF of 332/409, 686/282 i.e 2/115338 easily. The following is the detailed procedure to determine the greatest common factor of fractions 332/409, 686/282.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 332/409,686/282
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 332/409,686/282, numerators are 332,686
Denominators are 409,282
The GCF of 332,686 is 2 .
LCM of 409,282 is 115338.
The greatest common factor of 332/409,686/282 = [GCF of 332,686]/[LCM of 409,282]= 2/115338
Therefore, the GCF of 332/409,686/282 is 2/115338.
To find the highest common factor of 332,686, we have to find the factors of both numbers and list the highest common factor.
The factors of 332 are 1, 2, 4, 83, 166, 332
The factors of 686 are 1, 2, 7, 14, 49, 98, 343, 686
The HCF of 332,686 is 2.
Lets's calculate GCF of 332,686
2 | 332, 686 |
166, 343 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 332
:1,2,4,83,166,332
Now, list down the factors of 686
:1,2,7,14,49,98,343,686
Greatest Common Factor
We found the factors 332,686 . The biggest common factor number is the GCF number.
So the greatest common factor 332,686 is 2.
Lets's calculate LCM of 409,282
Given numbers has no common factors except 1. So, there LCM is their product i.e 115338
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/115338
Therefore, the GCF of Fractions 332/409,686/282 is 2/115338
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 409,282 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(409,282) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(409,282) x common factors =1 x 1 = 1
LCM(409,282) = ( 409 × 282 ) / 1
LCM(409,282) = 115338 / 1
LCM(409,282) = 115338
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 332,686?
The HCF of 332,686 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 332/409, 686/282?
Answer: GCF of Numerators as per given numbers 332/409, 686/282 is
GCF of Numerators i.e. for 332,686 is 2
LCM of denominators i.e. for 409,282 is 115338.
Thus, GCF of Fractions is 2/115338.Finally, GCF of Fractions for 332/409, 686/282 is 2/115338.