GCF of 450/323, 408/782
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 450/323, 408/782 i.e 6/14858 easily. The following is the detailed procedure to determine the greatest common factor of fractions 450/323, 408/782.
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 450/323,408/782?
Given fractions are 450/323,408/782
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 450/323,408/782, numerators are 450,408
Denominators are 323,782
The GCF of 450,408 is 6 .
LCM of 323,782 is 14858.
The greatest common factor of 450/323,408/782 = [GCF of 450,408]/[LCM of 323,782]= 6/14858
Therefore, the GCF of 450/323,408/782 is 6/14858.
To find the highest common factor of 450,408, we have to find the factors of both numbers and list the highest common factor.
The factors of 450 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, 450
The factors of 408 are 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, 408
The HCF of 450,408 is 6.
Lets's calculate GCF of 450,408
| 2 | 450, 408 |
| 3 | 225, 204 |
| 75, 68 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Greatest Common Factor of 450,408 By Matching Biggest Common Factor Method
Now, list down the factors of 450
:1,2,3,5,6,9,10,15,18,25,30,45,50,75,90,150,225,450
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 450,408 . The biggest common factor number is the GCF number.
So the greatest common factor 450,408 is 6.
Lets's calculate LCM of 323,782
| 17 | 323, 782 |
| 19, 46 |
∴ So the LCM of the given numbers is 17 x 19 x 46 = 14858
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/14858
Therefore, the GCF of Fractions 450/323,408/782 is 6/14858
Least Common Multiple of 323,782 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 323,782 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(323,782) = 17
common factors(in case of two or more numbers have common factors) = 1
GCF(323,782) x common factors =17 x 1 = 17
LCM(323,782) = ( 323 × 782 ) / 17
LCM(323,782) = 252586 / 17
LCM(323,782) = 14858
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FAQs on GCF of Fractions of 450/323, 408/782
1. What is the HCF of 450,408?
The HCF of 450,408 is 6
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 450/323, 408/782?
Answer: GCF of Numerators as per given numbers 450/323, 408/782 is
GCF of Numerators i.e. for 450,408 is 6
LCM of denominators i.e. for 323,782 is 14858.
Thus, GCF of Fractions is 6/14858.Finally, GCF of Fractions for 450/323, 408/782 is 6/14858.