Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 21/35,84/74,45/35
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 21,84,45
Greatest Common Factor of Numerators i.e. GCF of 21,84,45 is 3 .
LCM of Denominators means LCM of 35,74,35 as per the given fractions.
LCM of 35,74,35 is 2590 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 21,84,45
3 | 21, 84, 45 |
7, 28, 15 |
∴ So the GCF of the given numbers is 3 = 3
Factors of 21
List of positive integer factors of 21 that divides 21 without a remainder.
1,3,7,21
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 45
List of positive integer factors of 45 that divides 45 without a remainder.
1,3,5,9,15,45
Greatest Common Factor
We found the factors 21,84,45 . The biggest common factor number is the GCF number.
So the greatest common factor 21,84,45 is 3.
Lets's calculate LCM of 35,74,35
5 | 35, 74, 35 |
7 | 7, 74, 7 |
1, 74, 1 |
∴ So the LCM of the given numbers is 5 x 7 x 1 x 74 x 1 = 2590
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/2590
Therefore, the GCF of Fractions 21/35,84/74,45/35 is 3/2590
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 35,74,35 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(35,74,35) = 1
common factors(in case of two or more numbers have common factors) = 35
GCF(35,74,35) x common factors =1 x 35 = 35
LCM(35,74,35) = ( 35 × 74 × 35 ) / 35
LCM(35,74,35) = 90650 / 35
LCM(35,74,35) = 2590
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 21/35, 84/74, 45/35?
Answer: GCF of Numerators as per given numbers 21/35, 84/74, 45/35 is
GCF of Numerators i.e. for 21,84,45 is 3
LCM of denominators i.e. for 35,74,35 is 2590.
Thus, GCF of Fractions is 3/2590.Finally, GCF of Fractions for 21/35, 84/74, 45/35 is 3/2590.