GCF of 480/344, 408/556
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 480/344, 408/556 i.e 24/47816 easily. The following is the detailed procedure to determine the greatest common factor of fractions 480/344, 408/556.
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 480/344,408/556?
Given fractions are 480/344,408/556
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 480/344,408/556, numerators are 480,408
Denominators are 344,556
The GCF of 480,408 is 24 .
LCM of 344,556 is 47816.
The greatest common factor of 480/344,408/556 = [GCF of 480,408]/[LCM of 344,556]= 24/47816
Therefore, the GCF of 480/344,408/556 is 24/47816.
To find the highest common factor of 480,408, we have to find the factors of both numbers and list the highest common factor.
The factors of 480 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 80, 96, 120, 160, 240, 480
The factors of 408 are 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, 408
The HCF of 480,408 is 24.
Lets's calculate GCF of 480,408
| 2 | 480, 408 |
| 2 | 240, 204 |
| 2 | 120, 102 |
| 3 | 60, 51 |
| 20, 17 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 3 = 24
Greatest Common Factor of 480,408 By Matching Biggest Common Factor Method
Now, list down the factors of 480
:1,2,3,4,5,6,8,10,12,15,16,20,24,30,32,40,48,60,80,96,120,160,240,480
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 480,408 . The biggest common factor number is the GCF number.
So the greatest common factor 480,408 is 24.
Lets's calculate LCM of 344,556
| 2 | 344, 556 |
| 2 | 172, 278 |
| 86, 139 |
∴ So the LCM of the given numbers is 2 x 2 x 86 x 139 = 47816
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 24/47816
Therefore, the GCF of Fractions 480/344,408/556 is 24/47816
Least Common Multiple of 344,556 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 344,556 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(344,556) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(344,556) x common factors =4 x 1 = 4
LCM(344,556) = ( 344 × 556 ) / 4
LCM(344,556) = 191264 / 4
LCM(344,556) = 47816
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FAQs on GCF of Fractions of 480/344, 408/556
1. What is the HCF of 480,408?
The HCF of 480,408 is 24
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 480/344, 408/556?
Answer: GCF of Numerators as per given numbers 480/344, 408/556 is
GCF of Numerators i.e. for 480,408 is 24
LCM of denominators i.e. for 344,556 is 47816.
Thus, GCF of Fractions is 24/47816.Finally, GCF of Fractions for 480/344, 408/556 is 24/47816.