GCF of 513/210, 4560/348
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 513/210, 4560/348 i.e 57/12180 easily. The following is the detailed procedure to determine the greatest common factor of fractions 513/210, 4560/348.
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 513/210,4560/348?
Given fractions are 513/210,4560/348
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 513/210,4560/348, numerators are 513,4560
Denominators are 210,348
The GCF of 513,4560 is 57 .
LCM of 210,348 is 12180.
The greatest common factor of 513/210,4560/348 = [GCF of 513,4560]/[LCM of 210,348]= 57/12180
Therefore, the GCF of 513/210,4560/348 is 57/12180.
To find the highest common factor of 513,4560, we have to find the factors of both numbers and list the highest common factor.
The factors of 513 are 1, 3, 9, 19, 27, 57, 171, 513
The factors of 4560 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 19, 20, 24, 30, 38, 40, 48, 57, 60, 76, 80, 95, 114, 120, 152, 190, 228, 240, 285, 304, 380, 456, 570, 760, 912, 1140, 1520, 2280, 4560
The HCF of 513,4560 is 57.
Lets's calculate GCF of 513,4560
| 3 | 513, 4560 |
| 19 | 171, 1520 |
| 9, 80 |
∴ So the GCF of the given numbers is 3 x 19 = 57
Greatest Common Factor of 513,4560 By Matching Biggest Common Factor Method
Now, list down the factors of 513
:1,3,9,19,27,57,171,513
Now, list down the factors of 4560
:1,2,3,4,5,6,8,10,12,15,16,19,20,24,30,38,40,48,57,60,76,80,95,114,120,152,190,228,240,285,304,380,456,570,760,912,1140,1520,2280,4560
Greatest Common Factor
We found the factors 513,4560 . The biggest common factor number is the GCF number.
So the greatest common factor 513,4560 is 57.
Lets's calculate LCM of 210,348
| 2 | 210, 348 |
| 3 | 105, 174 |
| 35, 58 |
∴ So the LCM of the given numbers is 2 x 3 x 35 x 58 = 12180
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 57/12180
Therefore, the GCF of Fractions 513/210,4560/348 is 57/12180
Least Common Multiple of 210,348 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 210,348 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(210,348) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(210,348) x common factors =6 x 1 = 6
LCM(210,348) = ( 210 × 348 ) / 6
LCM(210,348) = 73080 / 6
LCM(210,348) = 12180
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FAQs on GCF of Fractions of 513/210, 4560/348
1. What is the HCF of 513,4560?
The HCF of 513,4560 is 57
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 513/210, 4560/348?
Answer: GCF of Numerators as per given numbers 513/210, 4560/348 is
GCF of Numerators i.e. for 513,4560 is 57
LCM of denominators i.e. for 210,348 is 12180.
Thus, GCF of Fractions is 57/12180.Finally, GCF of Fractions for 513/210, 4560/348 is 57/12180.