GCF of 1584/216, 8120/1728
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1584/216, 8120/1728 i.e 8/1728 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1584/216, 8120/1728.
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 1584/216,8120/1728?
Given fractions are 1584/216,8120/1728
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 1584/216,8120/1728, numerators are 1584,8120
Denominators are 216,1728
The GCF of 1584,8120 is 8 .
LCM of 216,1728 is 1728.
The greatest common factor of 1584/216,8120/1728 = [GCF of 1584,8120]/[LCM of 216,1728]= 8/1728
Therefore, the GCF of 1584/216,8120/1728 is 8/1728.
To find the highest common factor of 1584,8120, we have to find the factors of both numbers and list the highest common factor.
The factors of 1584 are 1, 2, 3, 4, 6, 8, 9, 11, 12, 16, 18, 22, 24, 33, 36, 44, 48, 66, 72, 88, 99, 132, 144, 176, 198, 264, 396, 528, 792, 1584
The factors of 8120 are 1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 29, 35, 40, 56, 58, 70, 116, 140, 145, 203, 232, 280, 290, 406, 580, 812, 1015, 1160, 1624, 2030, 4060, 8120
The HCF of 1584,8120 is 8.
Lets's calculate GCF of 1584,8120
| 2 | 1584, 8120 |
| 2 | 792, 4060 |
| 2 | 396, 2030 |
| 198, 1015 |
∴ So the GCF of the given numbers is 2 x 2 x 2 = 8
Greatest Common Factor of 1584,8120 By Matching Biggest Common Factor Method
Now, list down the factors of 1584
:1,2,3,4,6,8,9,11,12,16,18,22,24,33,36,44,48,66,72,88,99,132,144,176,198,264,396,528,792,1584
Now, list down the factors of 8120
:1,2,4,5,7,8,10,14,20,28,29,35,40,56,58,70,116,140,145,203,232,280,290,406,580,812,1015,1160,1624,2030,4060,8120
Greatest Common Factor
We found the factors 1584,8120 . The biggest common factor number is the GCF number.
So the greatest common factor 1584,8120 is 8.
Lets's calculate LCM of 216,1728
| 2 | 216, 1728 |
| 2 | 108, 864 |
| 2 | 54, 432 |
| 3 | 27, 216 |
| 3 | 9, 72 |
| 3 | 3, 24 |
| 1, 8 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 3 x 3 x 3 x 1 x 8 = 1728
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 8/1728
Therefore, the GCF of Fractions 1584/216,8120/1728 is 8/1728
Least Common Multiple of 216,1728 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 216,1728 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(216,1728) = 216
common factors(in case of two or more numbers have common factors) = 1
GCF(216,1728) x common factors =216 x 1 = 216
LCM(216,1728) = ( 216 × 1728 ) / 216
LCM(216,1728) = 373248 / 216
LCM(216,1728) = 1728
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FAQs on GCF of Fractions of 1584/216, 8120/1728
1. What is the HCF of 1584,8120?
The HCF of 1584,8120 is 8
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 1584/216, 8120/1728?
Answer: GCF of Numerators as per given numbers 1584/216, 8120/1728 is
GCF of Numerators i.e. for 1584,8120 is 8
LCM of denominators i.e. for 216,1728 is 1728.
Thus, GCF of Fractions is 8/1728.Finally, GCF of Fractions for 1584/216, 8120/1728 is 8/1728.