Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 824/35,822/62,400/42
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 824,822,400
Greatest Common Factor of Numerators i.e. GCF of 824,822,400 is 2 .
LCM of Denominators means LCM of 35,62,42 as per the given fractions.
LCM of 35,62,42 is 6510 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 824,822,400
2 | 824, 822, 400 |
412, 411, 200 |
∴ So the GCF of the given numbers is 2 = 2
Factors of 824
List of positive integer factors of 824 that divides 824 without a remainder.
1,2,4,8,103,206,412,824
Factors of 822
List of positive integer factors of 822 that divides 822 without a remainder.
1,2,3,6,137,274,411,822
Factors of 400
List of positive integer factors of 400 that divides 400 without a remainder.
1,2,4,5,8,10,16,20,25,40,50,80,100,200,400
Greatest Common Factor
We found the factors 824,822,400 . The biggest common factor number is the GCF number.
So the greatest common factor 824,822,400 is 2.
Lets's calculate LCM of 35,62,42
2 | 35, 62, 42 |
7 | 35, 31, 21 |
5, 31, 3 |
∴ So the LCM of the given numbers is 2 x 7 x 5 x 31 x 3 = 6510
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/6510
Therefore, the GCF of Fractions 824/35,822/62,400/42 is 2/6510
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 35,62,42 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(35,62,42) = 1
common factors(in case of two or more numbers have common factors) = 14
GCF(35,62,42) x common factors =1 x 14 = 14
LCM(35,62,42) = ( 35 × 62 × 42 ) / 14
LCM(35,62,42) = 91140 / 14
LCM(35,62,42) = 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 824/35, 822/62, 400/42?
Answer: GCF of Numerators as per given numbers 824/35, 822/62, 400/42 is
GCF of Numerators i.e. for 824,822,400 is 2
LCM of denominators i.e. for 35,62,42 is 6510.
Thus, GCF of Fractions is 2/6510.Finally, GCF of Fractions for 824/35, 822/62, 400/42 is 2/6510.