Use our free GCF of Fractions Calculator tool to compute the GCF of 828/104, 636/454 i.e 12/23608 easily. The following is the detailed procedure to determine the greatest common factor of fractions 828/104, 636/454.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 828/104,636/454
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 828/104,636/454, numerators are 828,636
Denominators are 104,454
The GCF of 828,636 is 12 .
LCM of 104,454 is 23608.
The greatest common factor of 828/104,636/454 = [GCF of 828,636]/[LCM of 104,454]= 12/23608
Therefore, the GCF of 828/104,636/454 is 12/23608.
To find the highest common factor of 828,636, we have to find the factors of both numbers and list the highest common factor.
The factors of 828 are 1, 2, 3, 4, 6, 9, 12, 18, 23, 36, 46, 69, 92, 138, 207, 276, 414, 828
The factors of 636 are 1, 2, 3, 4, 6, 12, 53, 106, 159, 212, 318, 636
The HCF of 828,636 is 12.
Lets's calculate GCF of 828,636
2 | 828, 636 |
2 | 414, 318 |
3 | 207, 159 |
69, 53 |
∴ So the GCF of the given numbers is 2 x 2 x 3 = 12
Now, list down the factors of 828
:1,2,3,4,6,9,12,18,23,36,46,69,92,138,207,276,414,828
Now, list down the factors of 636
:1,2,3,4,6,12,53,106,159,212,318,636
Greatest Common Factor
We found the factors 828,636 . The biggest common factor number is the GCF number.
So the greatest common factor 828,636 is 12.
Lets's calculate LCM of 104,454
2 | 104, 454 |
52, 227 |
∴ So the LCM of the given numbers is 2 x 52 x 227 = 23608
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 12/23608
Therefore, the GCF of Fractions 828/104,636/454 is 12/23608
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 104,454 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(104,454) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(104,454) x common factors =2 x 1 = 2
LCM(104,454) = ( 104 × 454 ) / 2
LCM(104,454) = 47216 / 2
LCM(104,454) = 23608
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 828,636?
The HCF of 828,636 is 12
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 828/104, 636/454?
Answer: GCF of Numerators as per given numbers 828/104, 636/454 is
GCF of Numerators i.e. for 828,636 is 12
LCM of denominators i.e. for 104,454 is 23608.
Thus, GCF of Fractions is 12/23608.Finally, GCF of Fractions for 828/104, 636/454 is 12/23608.