Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 14/40,23/92,62/20,335/84
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 14,23,62,335
Greatest Common Factor of Numerators i.e. GCF of 14,23,62,335 is 1 .
LCM of Denominators means LCM of 40,92,20,84 as per the given fractions.
LCM of 40,92,20,84 is 19320 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 14,23,62,335
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 14
List of positive integer factors of 14 that divides 14 without a remainder.
1,2,7,14
Factors of 23
List of positive integer factors of 23 that divides 23 without a remainder.
1,23
Factors of 62
List of positive integer factors of 62 that divides 62 without a remainder.
1,2,31,62
Factors of 335
List of positive integer factors of 335 that divides 335 without a remainder.
1,5,67,335
Greatest Common Factor
We found the factors 14,23,62,335 . The biggest common factor number is the GCF number.
So the greatest common factor 14,23,62,335 is 1.
Lets's calculate LCM of 40,92,20,84
2 | 40, 92, 20, 84 |
2 | 20, 46, 10, 42 |
5 | 5, 23, 10, 21 |
1, 23, 2, 21 |
∴ So the LCM of the given numbers is 2 x 2 x 5 x 1 x 23 x 2 x 21 = 19320
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/19320
Therefore, the GCF of Fractions 14/40,23/92,62/20,335/84 is 1/19320
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 40,92,20,84 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(40,92,20,84) = 4
common factors(in case of two or more numbers have common factors) = 80
GCF(40,92,20,84) x common factors =4 x 80 = 320
LCM(40,92,20,84) = ( 40 × 92 × 20 × 84 ) / 320
LCM(40,92,20,84) = 6182400 / 320
LCM(40,92,20,84) = 19320
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 14/40, 23/92, 62/20, 335/84?
Answer: GCF of Numerators as per given numbers 14/40, 23/92, 62/20, 335/84 is
GCF of Numerators i.e. for 14,23,62,335 is 1
LCM of denominators i.e. for 40,92,20,84 is 19320.
Thus, GCF of Fractions is 1/19320.Finally, GCF of Fractions for 14/40, 23/92, 62/20, 335/84 is 1/19320.