GCF of 2730/270, 8475/1410
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2730/270, 8475/1410 i.e 15/12690 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2730/270, 8475/1410.
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 2730/270,8475/1410?
Given fractions are 2730/270,8475/1410
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 2730/270,8475/1410, numerators are 2730,8475
Denominators are 270,1410
The GCF of 2730,8475 is 15 .
LCM of 270,1410 is 12690.
The greatest common factor of 2730/270,8475/1410 = [GCF of 2730,8475]/[LCM of 270,1410]= 15/12690
Therefore, the GCF of 2730/270,8475/1410 is 15/12690.
To find the highest common factor of 2730,8475, we have to find the factors of both numbers and list the highest common factor.
The factors of 2730 are 1, 2, 3, 5, 6, 7, 10, 13, 14, 15, 21, 26, 30, 35, 39, 42, 65, 70, 78, 91, 105, 130, 182, 195, 210, 273, 390, 455, 546, 910, 1365, 2730
The factors of 8475 are 1, 3, 5, 15, 25, 75, 113, 339, 565, 1695, 2825, 8475
The HCF of 2730,8475 is 15.
Lets's calculate GCF of 2730,8475
| 3 | 2730, 8475 |
| 5 | 910, 2825 |
| 182, 565 |
∴ So the GCF of the given numbers is 3 x 5 = 15
Greatest Common Factor of 2730,8475 By Matching Biggest Common Factor Method
Now, list down the factors of 2730
:1,2,3,5,6,7,10,13,14,15,21,26,30,35,39,42,65,70,78,91,105,130,182,195,210,273,390,455,546,910,1365,2730
Now, list down the factors of 8475
:1,3,5,15,25,75,113,339,565,1695,2825,8475
Greatest Common Factor
We found the factors 2730,8475 . The biggest common factor number is the GCF number.
So the greatest common factor 2730,8475 is 15.
Lets's calculate LCM of 270,1410
| 2 | 270, 1410 |
| 3 | 135, 705 |
| 5 | 45, 235 |
| 9, 47 |
∴ So the LCM of the given numbers is 2 x 3 x 5 x 9 x 47 = 12690
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 15/12690
Therefore, the GCF of Fractions 2730/270,8475/1410 is 15/12690
Least Common Multiple of 270,1410 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 270,1410 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(270,1410) = 30
common factors(in case of two or more numbers have common factors) = 1
GCF(270,1410) x common factors =30 x 1 = 30
LCM(270,1410) = ( 270 × 1410 ) / 30
LCM(270,1410) = 380700 / 30
LCM(270,1410) = 12690
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FAQs on GCF of Fractions of 2730/270, 8475/1410
1. What is the HCF of 2730,8475?
The HCF of 2730,8475 is 15
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 2730/270, 8475/1410?
Answer: GCF of Numerators as per given numbers 2730/270, 8475/1410 is
GCF of Numerators i.e. for 2730,8475 is 15
LCM of denominators i.e. for 270,1410 is 12690.
Thus, GCF of Fractions is 15/12690.Finally, GCF of Fractions for 2730/270, 8475/1410 is 15/12690.