Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 7/75,3/60,63/46,21/800
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 7,3,63,21
Greatest Common Factor of Numerators i.e. GCF of 7,3,63,21 is 1 .
LCM of Denominators means LCM of 75,60,46,800 as per the given fractions.
LCM of 75,60,46,800 is 55200 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 7,3,63,21
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 7
List of positive integer factors of 7 that divides 7 without a remainder.
1,7
Factors of 3
List of positive integer factors of 3 that divides 3 without a remainder.
1,3
Factors of 63
List of positive integer factors of 63 that divides 63 without a remainder.
1,3,7,9,21,63
Factors of 21
List of positive integer factors of 21 that divides 21 without a remainder.
1,3,7,21
Greatest Common Factor
We found the factors 7,3,63,21 . The biggest common factor number is the GCF number.
So the greatest common factor 7,3,63,21 is 1.
Lets's calculate LCM of 75,60,46,800
2 | 75, 60, 46, 800 |
2 | 75, 30, 23, 400 |
3 | 75, 15, 23, 200 |
5 | 25, 5, 23, 200 |
5 | 1, 5, 23, 40 |
1, 1, 23, 8 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 5 x 5 x 1 x 1 x 23 x 8 = 55200
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/55200
Therefore, the GCF of Fractions 7/75,3/60,63/46,21/800 is 1/55200
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 75,60,46,800 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(75,60,46,800) = 1
common factors(in case of two or more numbers have common factors) = 3000
GCF(75,60,46,800) x common factors =1 x 3000 = 3000
LCM(75,60,46,800) = ( 75 × 60 × 46 × 800 ) / 3000
LCM(75,60,46,800) = 165600000 / 3000
LCM(75,60,46,800) = 55200
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 7/75, 3/60, 63/46, 21/800?
Answer: GCF of Numerators as per given numbers 7/75, 3/60, 63/46, 21/800 is
GCF of Numerators i.e. for 7,3,63,21 is 1
LCM of denominators i.e. for 75,60,46,800 is 55200.
Thus, GCF of Fractions is 1/55200.Finally, GCF of Fractions for 7/75, 3/60, 63/46, 21/800 is 1/55200.