Use our free GCF of Fractions Calculator tool to compute the GCF of 100/266, 680/705 i.e 20/187530 easily. The following is the detailed procedure to determine the greatest common factor of fractions 100/266, 680/705.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 100/266,680/705
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 100/266,680/705, numerators are 100,680
Denominators are 266,705
The GCF of 100,680 is 20 .
LCM of 266,705 is 187530.
The greatest common factor of 100/266,680/705 = [GCF of 100,680]/[LCM of 266,705]= 20/187530
Therefore, the GCF of 100/266,680/705 is 20/187530.
To find the highest common factor of 100,680, 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 680 are 1, 2, 4, 5, 8, 10, 17, 20, 34, 40, 68, 85, 136, 170, 340, 680
The HCF of 100,680 is 20.
Lets's calculate GCF of 100,680
2 | 100, 680 |
2 | 50, 340 |
5 | 25, 170 |
5, 34 |
∴ So the GCF of the given numbers is 2 x 2 x 5 = 20
Now, list down the factors of 100
:1,2,4,5,10,20,25,50,100
Now, list down the factors of 680
:1,2,4,5,8,10,17,20,34,40,68,85,136,170,340,680
Greatest Common Factor
We found the factors 100,680 . The biggest common factor number is the GCF number.
So the greatest common factor 100,680 is 20.
Lets's calculate LCM of 266,705
Given numbers has no common factors except 1. So, there LCM is their product i.e 187530
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 20/187530
Therefore, the GCF of Fractions 100/266,680/705 is 20/187530
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 266,705 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(266,705) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(266,705) x common factors =1 x 1 = 1
LCM(266,705) = ( 266 × 705 ) / 1
LCM(266,705) = 187530 / 1
LCM(266,705) = 187530
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 100,680?
The HCF of 100,680 is 20
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 100/266, 680/705?
Answer: GCF of Numerators as per given numbers 100/266, 680/705 is
GCF of Numerators i.e. for 100,680 is 20
LCM of denominators i.e. for 266,705 is 187530.
Thus, GCF of Fractions is 20/187530.Finally, GCF of Fractions for 100/266, 680/705 is 20/187530.