GCF of 30/316, 105/374, 441/286
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 30/316, 105/374, 441/286 i.e 3/768196 easily. The following is the detailed procedure to determine the greatest common factor of fractions 30/316, 105/374, 441/286.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
What is the GCF of 30/316,105/374,441/286?
Given fractions are 30/316,105/374,441/286
To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by
GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators
In the fractions 30/316,105/374,441/286, numerators are 30,105,441
Denominators are 316,374,286
The GCF of 30,105,441 is 3 .
LCM of 316,374,286 is 768196.
The greatest common factor of 30/316,105/374,441/286 = [GCF of 30,105,441]/[LCM of 316,374,286]= 3/768196
Therefore, the GCF of 30/316,105/374,441/286 is 3/768196.
To find the highest common factor of 30,105,441, we have to find the factors of both numbers and list the highest common factor.
The factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30
The factors of 105 are 1, 3, 5, 7, 15, 21, 35, 105
The factors of 441 are 1, 3, 7, 9, 21, 49, 63, 147, 441
The HCF of 30,105,441 is 3.
Lets's calculate GCF of 30,105,441
| 3 | 30, 105, 441 |
| 10, 35, 147 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 30,105,441 By Matching Biggest Common Factor Method
Now, list down the factors of 30
:1,2,3,5,6,10,15,30
Now, list down the factors of 105
:1,3,5,7,15,21,35,105
Now, list down the factors of 441
:1,3,7,9,21,49,63,147,441
Greatest Common Factor
We found the factors 30,105,441 . The biggest common factor number is the GCF number.
So the greatest common factor 30,105,441 is 3.
Lets's calculate LCM of 316,374,286
| 2 | 316, 374, 286 |
| 11 | 158, 187, 143 |
| 158, 17, 13 |
∴ So the LCM of the given numbers is 2 x 11 x 158 x 17 x 13 = 768196
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/768196
Therefore, the GCF of Fractions 30/316,105/374,441/286 is 3/768196
Least Common Multiple of 316,374,286 with GCF Formula
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 316,374,286 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(316,374,286) = 2
common factors(in case of two or more numbers have common factors) = 22
GCF(316,374,286) x common factors =2 x 22 = 44
LCM(316,374,286) = ( 316 × 374 × 286 ) / 44
LCM(316,374,286) = 33800624 / 44
LCM(316,374,286) = 768196
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FAQs on GCF of Fractions of 30/316, 105/374, 441/286
1. What is the HCF of 30,105,441?
The HCF of 30,105,441 is 3
2. What is the GCF of a fraction?
The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.
3. 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.
4. What is the GCF of Fractions for 30/316, 105/374, 441/286?
Answer: GCF of Numerators as per given numbers 30/316, 105/374, 441/286 is
GCF of Numerators i.e. for 30,105,441 is 3
LCM of denominators i.e. for 316,374,286 is 768196.
Thus, GCF of Fractions is 3/768196.Finally, GCF of Fractions for 30/316, 105/374, 441/286 is 3/768196.