Use our free GCF of Fractions Calculator tool to compute the GCF of 100/135, 828/680 i.e 4/18360 easily. The following is the detailed procedure to determine the greatest common factor of fractions 100/135, 828/680.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 100/135,828/680
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 100/135,828/680, numerators are 100,828
Denominators are 135,680
The GCF of 100,828 is 4 .
LCM of 135,680 is 18360.
The greatest common factor of 100/135,828/680 = [GCF of 100,828]/[LCM of 135,680]= 4/18360
Therefore, the GCF of 100/135,828/680 is 4/18360.
To find the highest common factor of 100,828, we have to find the factors of both numbers and list the highest common factor.
The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, 100
The factors of 828 are 1, 2, 3, 4, 6, 9, 12, 18, 23, 36, 46, 69, 92, 138, 207, 276, 414, 828
The HCF of 100,828 is 4.
Lets's calculate GCF of 100,828
2 | 100, 828 |
2 | 50, 414 |
25, 207 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Now, list down the factors of 100
:1,2,4,5,10,20,25,50,100
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
Greatest Common Factor
We found the factors 100,828 . The biggest common factor number is the GCF number.
So the greatest common factor 100,828 is 4.
Lets's calculate LCM of 135,680
5 | 135, 680 |
27, 136 |
∴ So the LCM of the given numbers is 5 x 27 x 136 = 18360
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/18360
Therefore, the GCF of Fractions 100/135,828/680 is 4/18360
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 135,680 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(135,680) = 5
common factors(in case of two or more numbers have common factors) = 1
GCF(135,680) x common factors =5 x 1 = 5
LCM(135,680) = ( 135 × 680 ) / 5
LCM(135,680) = 91800 / 5
LCM(135,680) = 18360
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 100,828?
The HCF of 100,828 is 4
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 100/135, 828/680?
Answer: GCF of Numerators as per given numbers 100/135, 828/680 is
GCF of Numerators i.e. for 100,828 is 4
LCM of denominators i.e. for 135,680 is 18360.
Thus, GCF of Fractions is 4/18360.Finally, GCF of Fractions for 100/135, 828/680 is 4/18360.