GCF of 5220/513, 5616/9705
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 5220/513, 5616/9705 i.e 36/1659555 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5220/513, 5616/9705.
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 5220/513,5616/9705?
Given fractions are 5220/513,5616/9705
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 5220/513,5616/9705, numerators are 5220,5616
Denominators are 513,9705
The GCF of 5220,5616 is 36 .
LCM of 513,9705 is 1659555.
The greatest common factor of 5220/513,5616/9705 = [GCF of 5220,5616]/[LCM of 513,9705]= 36/1659555
Therefore, the GCF of 5220/513,5616/9705 is 36/1659555.
To find the highest common factor of 5220,5616, we have to find the factors of both numbers and list the highest common factor.
The factors of 5220 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 29, 30, 36, 45, 58, 60, 87, 90, 116, 145, 174, 180, 261, 290, 348, 435, 522, 580, 870, 1044, 1305, 1740, 2610, 5220
The factors of 5616 are 1, 2, 3, 4, 6, 8, 9, 12, 13, 16, 18, 24, 26, 27, 36, 39, 48, 52, 54, 72, 78, 104, 108, 117, 144, 156, 208, 216, 234, 312, 351, 432, 468, 624, 702, 936, 1404, 1872, 2808, 5616
The HCF of 5220,5616 is 36.
Lets's calculate GCF of 5220,5616
| 2 | 5220, 5616 |
| 2 | 2610, 2808 |
| 3 | 1305, 1404 |
| 3 | 435, 468 |
| 145, 156 |
∴ So the GCF of the given numbers is 2 x 2 x 3 x 3 = 36
Greatest Common Factor of 5220,5616 By Matching Biggest Common Factor Method
Now, list down the factors of 5220
:1,2,3,4,5,6,9,10,12,15,18,20,29,30,36,45,58,60,87,90,116,145,174,180,261,290,348,435,522,580,870,1044,1305,1740,2610,5220
Now, list down the factors of 5616
:1,2,3,4,6,8,9,12,13,16,18,24,26,27,36,39,48,52,54,72,78,104,108,117,144,156,208,216,234,312,351,432,468,624,702,936,1404,1872,2808,5616
Greatest Common Factor
We found the factors 5220,5616 . The biggest common factor number is the GCF number.
So the greatest common factor 5220,5616 is 36.
Lets's calculate LCM of 513,9705
| 3 | 513, 9705 |
| 171, 3235 |
∴ So the LCM of the given numbers is 3 x 171 x 3235 = 1659555
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 36/1659555
Therefore, the GCF of Fractions 5220/513,5616/9705 is 36/1659555
Least Common Multiple of 513,9705 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 513,9705 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(513,9705) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(513,9705) x common factors =3 x 1 = 3
LCM(513,9705) = ( 513 × 9705 ) / 3
LCM(513,9705) = 4978665 / 3
LCM(513,9705) = 1659555
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FAQs on GCF of Fractions of 5220/513, 5616/9705
1. What is the HCF of 5220,5616?
The HCF of 5220,5616 is 36
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 5220/513, 5616/9705?
Answer: GCF of Numerators as per given numbers 5220/513, 5616/9705 is
GCF of Numerators i.e. for 5220,5616 is 36
LCM of denominators i.e. for 513,9705 is 1659555.
Thus, GCF of Fractions is 36/1659555.Finally, GCF of Fractions for 5220/513, 5616/9705 is 36/1659555.