Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 402/83,142/84,224/750
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 402,142,224
Greatest Common Factor of Numerators i.e. GCF of 402,142,224 is 2 .
LCM of Denominators means LCM of 83,84,750 as per the given fractions.
LCM of 83,84,750 is 871500 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 402,142,224
2 | 402, 142, 224 |
201, 71, 112 |
∴ So the GCF of the given numbers is 2 = 2
Factors of 402
List of positive integer factors of 402 that divides 402 without a remainder.
1,2,3,6,67,134,201,402
Factors of 142
List of positive integer factors of 142 that divides 142 without a remainder.
1,2,71,142
Factors of 224
List of positive integer factors of 224 that divides 224 without a remainder.
1,2,4,7,8,14,16,28,32,56,112,224
Greatest Common Factor
We found the factors 402,142,224 . The biggest common factor number is the GCF number.
So the greatest common factor 402,142,224 is 2.
Lets's calculate LCM of 83,84,750
2 | 83, 84, 750 |
3 | 83, 42, 375 |
83, 14, 125 |
∴ So the LCM of the given numbers is 2 x 3 x 83 x 14 x 125 = 871500
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/871500
Therefore, the GCF of Fractions 402/83,142/84,224/750 is 2/871500
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 83,84,750 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(83,84,750) = 1
common factors(in case of two or more numbers have common factors) = 6
GCF(83,84,750) x common factors =1 x 6 = 6
LCM(83,84,750) = ( 83 × 84 × 750 ) / 6
LCM(83,84,750) = 5229000 / 6
LCM(83,84,750) = 871500
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 402/83, 142/84, 224/750?
Answer: GCF of Numerators as per given numbers 402/83, 142/84, 224/750 is
GCF of Numerators i.e. for 402,142,224 is 2
LCM of denominators i.e. for 83,84,750 is 871500.
Thus, GCF of Fractions is 2/871500.Finally, GCF of Fractions for 402/83, 142/84, 224/750 is 2/871500.