Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 84/39,40/59,456/14
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 84,40,456
Greatest Common Factor of Numerators i.e. GCF of 84,40,456 is 4 .
LCM of Denominators means LCM of 39,59,14 as per the given fractions.
LCM of 39,59,14 is 32214 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 84,40,456
2 | 84, 40, 456 |
2 | 42, 20, 228 |
21, 10, 114 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Factors of 84
List of positive integer factors of 84 that divides 84 without a remainder.
1,2,3,4,6,7,12,14,21,28,42,84
Factors of 40
List of positive integer factors of 40 that divides 40 without a remainder.
1,2,4,5,8,10,20,40
Factors of 456
List of positive integer factors of 456 that divides 456 without a remainder.
1,2,3,4,6,8,12,19,24,38,57,76,114,152,228,456
Greatest Common Factor
We found the factors 84,40,456 . The biggest common factor number is the GCF number.
So the greatest common factor 84,40,456 is 4.
Lets's calculate LCM of 39,59,14
Given numbers has no common factors except 1. So, there LCM is their product i.e 32214
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/32214
Therefore, the GCF of Fractions 84/39,40/59,456/14 is 4/32214
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 39,59,14 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(39,59,14) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(39,59,14) x common factors =1 x 1 = 1
LCM(39,59,14) = ( 39 × 59 × 14 ) / 1
LCM(39,59,14) = 32214 / 1
LCM(39,59,14) = 32214
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 84/39, 40/59, 456/14?
Answer: GCF of Numerators as per given numbers 84/39, 40/59, 456/14 is
GCF of Numerators i.e. for 84,40,456 is 4
LCM of denominators i.e. for 39,59,14 is 32214.
Thus, GCF of Fractions is 4/32214.Finally, GCF of Fractions for 84/39, 40/59, 456/14 is 4/32214.