GCF of 324/27, 414/884
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 324/27, 414/884 i.e 18/23868 easily. The following is the detailed procedure to determine the greatest common factor of fractions 324/27, 414/884.
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 324/27,414/884?
Given fractions are 324/27,414/884
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 324/27,414/884, numerators are 324,414
Denominators are 27,884
The GCF of 324,414 is 18 .
LCM of 27,884 is 23868.
The greatest common factor of 324/27,414/884 = [GCF of 324,414]/[LCM of 27,884]= 18/23868
Therefore, the GCF of 324/27,414/884 is 18/23868.
To find the highest common factor of 324,414, we have to find the factors of both numbers and list the highest common factor.
The factors of 324 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 324
The factors of 414 are 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414
The HCF of 324,414 is 18.
Lets's calculate GCF of 324,414
| 2 | 324, 414 |
| 3 | 162, 207 |
| 3 | 54, 69 |
| 18, 23 |
∴ So the GCF of the given numbers is 2 x 3 x 3 = 18
Greatest Common Factor of 324,414 By Matching Biggest Common Factor Method
Now, list down the factors of 324
:1,2,3,4,6,9,12,18,27,36,54,81,108,162,324
Now, list down the factors of 414
:1,2,3,6,9,18,23,46,69,138,207,414
Greatest Common Factor
We found the factors 324,414 . The biggest common factor number is the GCF number.
So the greatest common factor 324,414 is 18.
Lets's calculate LCM of 27,884
Given numbers has no common factors except 1. So, there LCM is their product i.e 23868
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 18/23868
Therefore, the GCF of Fractions 324/27,414/884 is 18/23868
Least Common Multiple of 27,884 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 27,884 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(27,884) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(27,884) x common factors =1 x 1 = 1
LCM(27,884) = ( 27 × 884 ) / 1
LCM(27,884) = 23868 / 1
LCM(27,884) = 23868
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FAQs on GCF of Fractions of 324/27, 414/884
1. What is the HCF of 324,414?
The HCF of 324,414 is 18
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 324/27, 414/884?
Answer: GCF of Numerators as per given numbers 324/27, 414/884 is
GCF of Numerators i.e. for 324,414 is 18
LCM of denominators i.e. for 27,884 is 23868.
Thus, GCF of Fractions is 18/23868.Finally, GCF of Fractions for 324/27, 414/884 is 18/23868.