GCF of 1530/124, 8160/582
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1530/124, 8160/582 i.e 510/36084 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1530/124, 8160/582.
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 1530/124,8160/582?
Given fractions are 1530/124,8160/582
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 1530/124,8160/582, numerators are 1530,8160
Denominators are 124,582
The GCF of 1530,8160 is 510 .
LCM of 124,582 is 36084.
The greatest common factor of 1530/124,8160/582 = [GCF of 1530,8160]/[LCM of 124,582]= 510/36084
Therefore, the GCF of 1530/124,8160/582 is 510/36084.
To find the highest common factor of 1530,8160, we have to find the factors of both numbers and list the highest common factor.
The factors of 1530 are 1, 2, 3, 5, 6, 9, 10, 15, 17, 18, 30, 34, 45, 51, 85, 90, 102, 153, 170, 255, 306, 510, 765, 1530
The factors of 8160 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 17, 20, 24, 30, 32, 34, 40, 48, 51, 60, 68, 80, 85, 96, 102, 120, 136, 160, 170, 204, 240, 255, 272, 340, 408, 480, 510, 544, 680, 816, 1020, 1360, 1632, 2040, 2720, 4080, 8160
The HCF of 1530,8160 is 510.
Lets's calculate GCF of 1530,8160
| 2 | 1530, 8160 |
| 3 | 765, 4080 |
| 5 | 255, 1360 |
| 17 | 51, 272 |
| 3, 16 |
∴ So the GCF of the given numbers is 2 x 3 x 5 x 17 = 510
Greatest Common Factor of 1530,8160 By Matching Biggest Common Factor Method
Now, list down the factors of 1530
:1,2,3,5,6,9,10,15,17,18,30,34,45,51,85,90,102,153,170,255,306,510,765,1530
Now, list down the factors of 8160
:1,2,3,4,5,6,8,10,12,15,16,17,20,24,30,32,34,40,48,51,60,68,80,85,96,102,120,136,160,170,204,240,255,272,340,408,480,510,544,680,816,1020,1360,1632,2040,2720,4080,8160
Greatest Common Factor
We found the factors 1530,8160 . The biggest common factor number is the GCF number.
So the greatest common factor 1530,8160 is 510.
Lets's calculate LCM of 124,582
| 2 | 124, 582 |
| 62, 291 |
∴ So the LCM of the given numbers is 2 x 62 x 291 = 36084
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 510/36084
Therefore, the GCF of Fractions 1530/124,8160/582 is 510/36084
Least Common Multiple of 124,582 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 124,582 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(124,582) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(124,582) x common factors =2 x 1 = 2
LCM(124,582) = ( 124 × 582 ) / 2
LCM(124,582) = 72168 / 2
LCM(124,582) = 36084
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 1530/124, 8160/582
1. What is the HCF of 1530,8160?
The HCF of 1530,8160 is 510
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 1530/124, 8160/582?
Answer: GCF of Numerators as per given numbers 1530/124, 8160/582 is
GCF of Numerators i.e. for 1530,8160 is 510
LCM of denominators i.e. for 124,582 is 36084.
Thus, GCF of Fractions is 510/36084.Finally, GCF of Fractions for 1530/124, 8160/582 is 510/36084.