Use our free GCF of Fractions Calculator tool to compute the GCF of 32/121, 762/691, 684/401 i.e 2/33528011 easily. The following is the detailed procedure to determine the greatest common factor of fractions 32/121, 762/691, 684/401.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 32/121,762/691,684/401
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 32/121,762/691,684/401, numerators are 32,762,684
Denominators are 121,691,401
The GCF of 32,762,684 is 2 .
LCM of 121,691,401 is 33528011.
The greatest common factor of 32/121,762/691,684/401 = [GCF of 32,762,684]/[LCM of 121,691,401]= 2/33528011
Therefore, the GCF of 32/121,762/691,684/401 is 2/33528011.
To find the highest common factor of 32,762,684, we have to find the factors of both numbers and list the highest common factor.
The factors of 32 are 1, 2, 4, 8, 16, 32
The factors of 762 are 1, 2, 3, 6, 127, 254, 381, 762
The factors of 684 are 1, 2, 3, 4, 6, 9, 12, 18, 19, 36, 38, 57, 76, 114, 171, 228, 342, 684
The HCF of 32,762,684 is 2.
Lets's calculate GCF of 32,762,684
2 | 32, 762, 684 |
16, 381, 342 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 32
:1,2,4,8,16,32
Now, list down the factors of 762
:1,2,3,6,127,254,381,762
Now, list down the factors of 684
:1,2,3,4,6,9,12,18,19,36,38,57,76,114,171,228,342,684
Greatest Common Factor
We found the factors 32,762,684 . The biggest common factor number is the GCF number.
So the greatest common factor 32,762,684 is 2.
Lets's calculate LCM of 121,691,401
Given numbers has no common factors except 1. So, there LCM is their product i.e 33528011
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/33528011
Therefore, the GCF of Fractions 32/121,762/691,684/401 is 2/33528011
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 121,691,401 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(121,691,401) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(121,691,401) x common factors =1 x 1 = 1
LCM(121,691,401) = ( 121 × 691 × 401 ) / 1
LCM(121,691,401) = 33528011 / 1
LCM(121,691,401) = 33528011
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 32,762,684?
The HCF of 32,762,684 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 32/121, 762/691, 684/401?
Answer: GCF of Numerators as per given numbers 32/121, 762/691, 684/401 is
GCF of Numerators i.e. for 32,762,684 is 2
LCM of denominators i.e. for 121,691,401 is 33528011.
Thus, GCF of Fractions is 2/33528011.Finally, GCF of Fractions for 32/121, 762/691, 684/401 is 2/33528011.