Use our free GCF of Fractions Calculator tool to compute the GCF of 416/212, 141/382 i.e 1/40492 easily. The following is the detailed procedure to determine the greatest common factor of fractions 416/212, 141/382.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 416/212,141/382
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 416/212,141/382, numerators are 416,141
Denominators are 212,382
The GCF of 416,141 is 1 .
LCM of 212,382 is 40492.
The greatest common factor of 416/212,141/382 = [GCF of 416,141]/[LCM of 212,382]= 1/40492
Therefore, the GCF of 416/212,141/382 is 1/40492.
To find the highest common factor of 416,141, we have to find the factors of both numbers and list the highest common factor.
The factors of 416 are 1, 2, 4, 8, 13, 16, 26, 32, 52, 104, 208, 416
The factors of 141 are 1, 3, 47, 141
The HCF of 416,141 is 1.
Lets's calculate GCF of 416,141
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 416
:1,2,4,8,13,16,26,32,52,104,208,416
Now, list down the factors of 141
:1,3,47,141
Greatest Common Factor
We found the factors 416,141 . The biggest common factor number is the GCF number.
So the greatest common factor 416,141 is 1.
Lets's calculate LCM of 212,382
2 | 212, 382 |
106, 191 |
∴ So the LCM of the given numbers is 2 x 106 x 191 = 40492
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/40492
Therefore, the GCF of Fractions 416/212,141/382 is 1/40492
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 212,382 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(212,382) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(212,382) x common factors =2 x 1 = 2
LCM(212,382) = ( 212 × 382 ) / 2
LCM(212,382) = 80984 / 2
LCM(212,382) = 40492
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 416,141?
The HCF of 416,141 is 1
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 416/212, 141/382?
Answer: GCF of Numerators as per given numbers 416/212, 141/382 is
GCF of Numerators i.e. for 416,141 is 1
LCM of denominators i.e. for 212,382 is 40492.
Thus, GCF of Fractions is 1/40492.Finally, GCF of Fractions for 416/212, 141/382 is 1/40492.