GCF of 412/33, 408/498
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 412/33, 408/498 i.e 4/5478 easily. The following is the detailed procedure to determine the greatest common factor of fractions 412/33, 408/498.
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 412/33,408/498?
Given fractions are 412/33,408/498
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 412/33,408/498, numerators are 412,408
Denominators are 33,498
The GCF of 412,408 is 4 .
LCM of 33,498 is 5478.
The greatest common factor of 412/33,408/498 = [GCF of 412,408]/[LCM of 33,498]= 4/5478
Therefore, the GCF of 412/33,408/498 is 4/5478.
To find the highest common factor of 412,408, we have to find the factors of both numbers and list the highest common factor.
The factors of 412 are 1, 2, 4, 103, 206, 412
The factors of 408 are 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, 408
The HCF of 412,408 is 4.
Lets's calculate GCF of 412,408
| 2 | 412, 408 |
| 2 | 206, 204 |
| 103, 102 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Greatest Common Factor of 412,408 By Matching Biggest Common Factor Method
Now, list down the factors of 412
:1,2,4,103,206,412
Now, list down the factors of 408
:1,2,3,4,6,8,12,17,24,34,51,68,102,136,204,408
Greatest Common Factor
We found the factors 412,408 . The biggest common factor number is the GCF number.
So the greatest common factor 412,408 is 4.
Lets's calculate LCM of 33,498
| 3 | 33, 498 |
| 11, 166 |
∴ So the LCM of the given numbers is 3 x 11 x 166 = 5478
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/5478
Therefore, the GCF of Fractions 412/33,408/498 is 4/5478
Least Common Multiple of 33,498 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 33,498 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(33,498) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(33,498) x common factors =3 x 1 = 3
LCM(33,498) = ( 33 × 498 ) / 3
LCM(33,498) = 16434 / 3
LCM(33,498) = 5478
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FAQs on GCF of Fractions of 412/33, 408/498
1. What is the HCF of 412,408?
The HCF of 412,408 is 4
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 412/33, 408/498?
Answer: GCF of Numerators as per given numbers 412/33, 408/498 is
GCF of Numerators i.e. for 412,408 is 4
LCM of denominators i.e. for 33,498 is 5478.
Thus, GCF of Fractions is 4/5478.Finally, GCF of Fractions for 412/33, 408/498 is 4/5478.