Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 75/175,125/343,150/490
Formula to find GCF of Fractions is
GCF = GCF of Numerators/LCM of Denominators
As per the formula GCF of Fractions let’s split into two parts and find the GCF of Numerators and LCM of Denominators
In the given fractions GCF of Numerators means GCF of 75,125,150
Greatest Common Factor of Numerators i.e. GCF of 75,125,150 is 25 .
LCM of Denominators means LCM of 175,343,490 as per the given fractions.
LCM of 175,343,490 is 17150 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 75,125,150
5 | 75, 125, 150 |
5 | 15, 25, 30 |
3, 5, 6 |
∴ So the GCF of the given numbers is 5 x 5 = 25
Factors of 75
List of positive integer factors of 75 that divides 75 without a remainder.
1,3,5,15,25,75
Factors of 125
List of positive integer factors of 125 that divides 125 without a remainder.
1,5,25,125
Factors of 150
List of positive integer factors of 150 that divides 150 without a remainder.
1,2,3,5,6,10,15,25,30,50,75,150
Greatest Common Factor
We found the factors 75,125,150 . The biggest common factor number is the GCF number.
So the greatest common factor 75,125,150 is 25.
Lets's calculate LCM of 175,343,490
5 | 175, 343, 490 |
7 | 35, 343, 98 |
7 | 5, 49, 14 |
5, 7, 2 |
∴ So the LCM of the given numbers is 5 x 7 x 7 x 5 x 7 x 2 = 17150
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 25/17150
Therefore, the GCF of Fractions 75/175,125/343,150/490 is 25/17150
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 175,343,490 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(175,343,490) = 7
common factors(in case of two or more numbers have common factors) = 245
GCF(175,343,490) x common factors =7 x 245 = 1715
LCM(175,343,490) = ( 175 × 343 × 490 ) / 1715
LCM(175,343,490) = 29412250 / 1715
LCM(175,343,490) = 17150
Here are some samples of GCF of Fractions calculations.
Here are some samples of GCF of Fractions calculations.
1. 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.
2. What is the GCF of Fractions for 75/175, 125/343, 150/490?
Answer: GCF of Numerators as per given numbers 75/175, 125/343, 150/490 is
GCF of Numerators i.e. for 75,125,150 is 25
LCM of denominators i.e. for 175,343,490 is 17150.
Thus, GCF of Fractions is 25/17150.Finally, GCF of Fractions for 75/175, 125/343, 150/490 is 25/17150.