GCF of 3/84, 3/36, 9/48, 14/406
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 3/84, 3/36, 9/48, 14/406 i.e 1/29232 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3/84, 3/36, 9/48, 14/406.
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 3/84,3/36,9/48,14/406?
Given fractions are 3/84,3/36,9/48,14/406
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 3/84,3/36,9/48,14/406, numerators are 3,3,9,14
Denominators are 84,36,48,406
The GCF of 3,3,9,14 is 1 .
LCM of 84,36,48,406 is 29232.
The greatest common factor of 3/84,3/36,9/48,14/406 = [GCF of 3,3,9,14]/[LCM of 84,36,48,406]= 1/29232
Therefore, the GCF of 3/84,3/36,9/48,14/406 is 1/29232.
To find the highest common factor of 3,3,9,14, we have to find the factors of both numbers and list the highest common factor.
The factors of 3 are 1, 3
The factors of 3 are 1, 3
The factors of 9 are 1, 3, 9
The factors of 14 are 1, 2, 7, 14
The HCF of 3,3,9,14 is 1.
Lets's calculate GCF of 3,3,9,14
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 3,3,9,14 By Matching Biggest Common Factor Method
Now, list down the factors of 3
:1,3
Now, list down the factors of 3
:1,3
Now, list down the factors of 9
:1,3,9
Now, list down the factors of 14
:1,2,7,14
Greatest Common Factor
We found the factors 3,3,9,14 . The biggest common factor number is the GCF number.
So the greatest common factor 3,3,9,14 is 1.
Lets's calculate LCM of 84,36,48,406
| 2 | 84, 36, 48, 406 |
| 2 | 42, 18, 24, 203 |
| 3 | 21, 9, 12, 203 |
| 7 | 7, 3, 4, 203 |
| 1, 3, 4, 29 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 7 x 1 x 3 x 4 x 29 = 29232
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/29232
Therefore, the GCF of Fractions 3/84,3/36,9/48,14/406 is 1/29232
Least Common Multiple of 84,36,48,406 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 84,36,48,406 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(84,36,48,406) = 2
common factors(in case of two or more numbers have common factors) = 1008
GCF(84,36,48,406) x common factors =2 x 1008 = 2016
LCM(84,36,48,406) = ( 84 × 36 × 48 × 406 ) / 2016
LCM(84,36,48,406) = 58931712 / 2016
LCM(84,36,48,406) = 29232
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 3/84, 3/36, 9/48, 14/406
1. What is the HCF of 3,3,9,14?
The HCF of 3,3,9,14 is 1
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 3/84, 3/36, 9/48, 14/406?
Answer: GCF of Numerators as per given numbers 3/84, 3/36, 9/48, 14/406 is
GCF of Numerators i.e. for 3,3,9,14 is 1
LCM of denominators i.e. for 84,36,48,406 is 29232.
Thus, GCF of Fractions is 1/29232.Finally, GCF of Fractions for 3/84, 3/36, 9/48, 14/406 is 1/29232.