Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 420/648,154/252
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 420,154
Greatest Common Factor of Numerators i.e. GCF of 420,154 is 14 .
LCM of Denominators means LCM of 648,252 as per the given fractions.
LCM of 648,252 is 4536 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 420,154
2 | 420, 154 |
7 | 210, 77 |
30, 11 |
∴ So the GCF of the given numbers is 2 x 7 = 14
Factors of 420
List of positive integer factors of 420 that divides 420 without a remainder.
1,2,3,4,5,6,7,10,12,14,15,20,21,28,30,35,42,60,70,84,105,140,210,420
Factors of 154
List of positive integer factors of 154 that divides 154 without a remainder.
1,2,7,11,14,22,77,154
Greatest Common Factor
We found the factors 420,154 . The biggest common factor number is the GCF number.
So the greatest common factor 420,154 is 14.
Lets's calculate LCM of 648,252
2 | 648, 252 |
2 | 324, 126 |
3 | 162, 63 |
3 | 54, 21 |
18, 7 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 3 x 18 x 7 = 4536
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/4536
Therefore, the GCF of Fractions 420/648,154/252 is 14/4536
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 648,252 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(648,252) = 36
common factors(in case of two or more numbers have common factors) = 1
GCF(648,252) x common factors =36 x 1 = 36
LCM(648,252) = ( 648 × 252 ) / 36
LCM(648,252) = 163296 / 36
LCM(648,252) = 4536
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 420/648, 154/252?
Answer: GCF of Numerators as per given numbers 420/648, 154/252 is
GCF of Numerators i.e. for 420,154 is 14
LCM of denominators i.e. for 648,252 is 4536.
Thus, GCF of Fractions is 14/4536.Finally, GCF of Fractions for 420/648, 154/252 is 14/4536.