Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 78/35,21/13,66/16,39/63
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 78,21,66,39
Greatest Common Factor of Numerators i.e. GCF of 78,21,66,39 is 3 .
LCM of Denominators means LCM of 35,13,16,63 as per the given fractions.
LCM of 35,13,16,63 is 65520 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 78,21,66,39
3 | 78, 21, 66, 39 |
26, 7, 22, 13 |
∴ So the GCF of the given numbers is 3 = 3
Factors of 78
List of positive integer factors of 78 that divides 78 without a remainder.
1,2,3,6,13,26,39,78
Factors of 21
List of positive integer factors of 21 that divides 21 without a remainder.
1,3,7,21
Factors of 66
List of positive integer factors of 66 that divides 66 without a remainder.
1,2,3,6,11,22,33,66
Factors of 39
List of positive integer factors of 39 that divides 39 without a remainder.
1,3,13,39
Greatest Common Factor
We found the factors 78,21,66,39 . The biggest common factor number is the GCF number.
So the greatest common factor 78,21,66,39 is 3.
Lets's calculate LCM of 35,13,16,63
7 | 35, 13, 16, 63 |
5, 13, 16, 9 |
∴ So the LCM of the given numbers is 7 x 5 x 13 x 16 x 9 = 65520
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/65520
Therefore, the GCF of Fractions 78/35,21/13,66/16,39/63 is 3/65520
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 35,13,16,63 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(35,13,16,63) = 1
common factors(in case of two or more numbers have common factors) = 7
GCF(35,13,16,63) x common factors =1 x 7 = 7
LCM(35,13,16,63) = ( 35 × 13 × 16 × 63 ) / 7
LCM(35,13,16,63) = 458640 / 7
LCM(35,13,16,63) = 65520
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 78/35, 21/13, 66/16, 39/63?
Answer: GCF of Numerators as per given numbers 78/35, 21/13, 66/16, 39/63 is
GCF of Numerators i.e. for 78,21,66,39 is 3
LCM of denominators i.e. for 35,13,16,63 is 65520.
Thus, GCF of Fractions is 3/65520.Finally, GCF of Fractions for 78/35, 21/13, 66/16, 39/63 is 3/65520.