Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 12/10,24/70,33/62,336/42
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 12,24,33,336
Greatest Common Factor of Numerators i.e. GCF of 12,24,33,336 is 3 .
LCM of Denominators means LCM of 10,70,62,42 as per the given fractions.
LCM of 10,70,62,42 is 6510 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 12,24,33,336
3 | 12, 24, 33, 336 |
4, 8, 11, 112 |
∴ So the GCF of the given numbers is 3 = 3
Factors of 12
List of positive integer factors of 12 that divides 12 without a remainder.
1,2,3,4,6,12
Factors of 24
List of positive integer factors of 24 that divides 24 without a remainder.
1,2,3,4,6,8,12,24
Factors of 33
List of positive integer factors of 33 that divides 33 without a remainder.
1,3,11,33
Factors of 336
List of positive integer factors of 336 that divides 336 without a remainder.
1,2,3,4,6,7,8,12,14,16,21,24,28,42,48,56,84,112,168,336
Greatest Common Factor
We found the factors 12,24,33,336 . The biggest common factor number is the GCF number.
So the greatest common factor 12,24,33,336 is 3.
Lets's calculate LCM of 10,70,62,42
2 | 10, 70, 62, 42 |
5 | 5, 35, 31, 21 |
7 | 1, 7, 31, 21 |
1, 1, 31, 3 |
∴ So the LCM of the given numbers is 2 x 5 x 7 x 1 x 1 x 31 x 3 = 6510
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/6510
Therefore, the GCF of Fractions 12/10,24/70,33/62,336/42 is 3/6510
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 10,70,62,42 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(10,70,62,42) = 2
common factors(in case of two or more numbers have common factors) = 140
GCF(10,70,62,42) x common factors =2 x 140 = 280
LCM(10,70,62,42) = ( 10 × 70 × 62 × 42 ) / 280
LCM(10,70,62,42) = 1822800 / 280
LCM(10,70,62,42) = 6510
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 12/10, 24/70, 33/62, 336/42?
Answer: GCF of Numerators as per given numbers 12/10, 24/70, 33/62, 336/42 is
GCF of Numerators i.e. for 12,24,33,336 is 3
LCM of denominators i.e. for 10,70,62,42 is 6510.
Thus, GCF of Fractions is 3/6510.Finally, GCF of Fractions for 12/10, 24/70, 33/62, 336/42 is 3/6510.