GCF of 2208/624, 5414/5616
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2208/624, 5414/5616 i.e 2/5616 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2208/624, 5414/5616.
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 2208/624,5414/5616?
Given fractions are 2208/624,5414/5616
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 2208/624,5414/5616, numerators are 2208,5414
Denominators are 624,5616
The GCF of 2208,5414 is 2 .
LCM of 624,5616 is 5616.
The greatest common factor of 2208/624,5414/5616 = [GCF of 2208,5414]/[LCM of 624,5616]= 2/5616
Therefore, the GCF of 2208/624,5414/5616 is 2/5616.
To find the highest common factor of 2208,5414, we have to find the factors of both numbers and list the highest common factor.
The factors of 2208 are 1, 2, 3, 4, 6, 8, 12, 16, 23, 24, 32, 46, 48, 69, 92, 96, 138, 184, 276, 368, 552, 736, 1104, 2208
The factors of 5414 are 1, 2, 2707, 5414
The HCF of 2208,5414 is 2.
Lets's calculate GCF of 2208,5414
| 2 | 2208, 5414 |
| 1104, 2707 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 2208,5414 By Matching Biggest Common Factor Method
Now, list down the factors of 2208
:1,2,3,4,6,8,12,16,23,24,32,46,48,69,92,96,138,184,276,368,552,736,1104,2208
Now, list down the factors of 5414
:1,2,2707,5414
Greatest Common Factor
We found the factors 2208,5414 . The biggest common factor number is the GCF number.
So the greatest common factor 2208,5414 is 2.
Lets's calculate LCM of 624,5616
| 2 | 624, 5616 |
| 2 | 312, 2808 |
| 2 | 156, 1404 |
| 2 | 78, 702 |
| 3 | 39, 351 |
| 13 | 13, 117 |
| 1, 9 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 3 x 13 x 1 x 9 = 5616
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/5616
Therefore, the GCF of Fractions 2208/624,5414/5616 is 2/5616
Least Common Multiple of 624,5616 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 624,5616 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(624,5616) = 624
common factors(in case of two or more numbers have common factors) = 1
GCF(624,5616) x common factors =624 x 1 = 624
LCM(624,5616) = ( 624 × 5616 ) / 624
LCM(624,5616) = 3504384 / 624
LCM(624,5616) = 5616
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 2208/624, 5414/5616
1. What is the HCF of 2208,5414?
The HCF of 2208,5414 is 2
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 2208/624, 5414/5616?
Answer: GCF of Numerators as per given numbers 2208/624, 5414/5616 is
GCF of Numerators i.e. for 2208,5414 is 2
LCM of denominators i.e. for 624,5616 is 5616.
Thus, GCF of Fractions is 2/5616.Finally, GCF of Fractions for 2208/624, 5414/5616 is 2/5616.