Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 340/549,402/864,414/784
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 340,402,414
Greatest Common Factor of Numerators i.e. GCF of 340,402,414 is 2 .
LCM of Denominators means LCM of 549,864,784 as per the given fractions.
LCM of 549,864,784 is 2582496 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 340,402,414
2 | 340, 402, 414 |
170, 201, 207 |
∴ So the GCF of the given numbers is 2 = 2
Factors of 340
List of positive integer factors of 340 that divides 340 without a remainder.
1,2,4,5,10,17,20,34,68,85,170,340
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 414
List of positive integer factors of 414 that divides 414 without a remainder.
1,2,3,6,9,18,23,46,69,138,207,414
Greatest Common Factor
We found the factors 340,402,414 . The biggest common factor number is the GCF number.
So the greatest common factor 340,402,414 is 2.
Lets's calculate LCM of 549,864,784
2 | 549, 864, 784 |
2 | 549, 432, 392 |
2 | 549, 216, 196 |
2 | 549, 108, 98 |
3 | 549, 54, 49 |
3 | 183, 18, 49 |
61, 6, 49 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 3 x 3 x 61 x 6 x 49 = 2582496
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/2582496
Therefore, the GCF of Fractions 340/549,402/864,414/784 is 2/2582496
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 549,864,784 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(549,864,784) = 1
common factors(in case of two or more numbers have common factors) = 144
GCF(549,864,784) x common factors =1 x 144 = 144
LCM(549,864,784) = ( 549 × 864 × 784 ) / 144
LCM(549,864,784) = 371879424 / 144
LCM(549,864,784) = 2582496
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 340/549, 402/864, 414/784?
Answer: GCF of Numerators as per given numbers 340/549, 402/864, 414/784 is
GCF of Numerators i.e. for 340,402,414 is 2
LCM of denominators i.e. for 549,864,784 is 2582496.
Thus, GCF of Fractions is 2/2582496.Finally, GCF of Fractions for 340/549, 402/864, 414/784 is 2/2582496.