Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 77/42,33/32,40/11,66/176
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 77,33,40,66
Greatest Common Factor of Numerators i.e. GCF of 77,33,40,66 is 1 .
LCM of Denominators means LCM of 42,32,11,176 as per the given fractions.
LCM of 42,32,11,176 is 7392 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 77,33,40,66
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 77
List of positive integer factors of 77 that divides 77 without a remainder.
1,7,11,77
Factors of 33
List of positive integer factors of 33 that divides 33 without a remainder.
1,3,11,33
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 66
List of positive integer factors of 66 that divides 66 without a remainder.
1,2,3,6,11,22,33,66
Greatest Common Factor
We found the factors 77,33,40,66 . The biggest common factor number is the GCF number.
So the greatest common factor 77,33,40,66 is 1.
Lets's calculate LCM of 42,32,11,176
2 | 42, 32, 11, 176 |
2 | 21, 16, 11, 88 |
2 | 21, 8, 11, 44 |
2 | 21, 4, 11, 22 |
11 | 21, 2, 11, 11 |
21, 2, 1, 1 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 11 x 21 x 2 x 1 x 1 = 7392
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/7392
Therefore, the GCF of Fractions 77/42,33/32,40/11,66/176 is 1/7392
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 42,32,11,176 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(42,32,11,176) = 1
common factors(in case of two or more numbers have common factors) = 352
GCF(42,32,11,176) x common factors =1 x 352 = 352
LCM(42,32,11,176) = ( 42 × 32 × 11 × 176 ) / 352
LCM(42,32,11,176) = 2601984 / 352
LCM(42,32,11,176) = 7392
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 77/42, 33/32, 40/11, 66/176?
Answer: GCF of Numerators as per given numbers 77/42, 33/32, 40/11, 66/176 is
GCF of Numerators i.e. for 77,33,40,66 is 1
LCM of denominators i.e. for 42,32,11,176 is 7392.
Thus, GCF of Fractions is 1/7392.Finally, GCF of Fractions for 77/42, 33/32, 40/11, 66/176 is 1/7392.