GCF of 304/206, 560/170
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 304/206, 560/170 i.e 16/17510 easily. The following is the detailed procedure to determine the greatest common factor of fractions 304/206, 560/170.
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 304/206,560/170?
Given fractions are 304/206,560/170
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 304/206,560/170, numerators are 304,560
Denominators are 206,170
The GCF of 304,560 is 16 .
LCM of 206,170 is 17510.
The greatest common factor of 304/206,560/170 = [GCF of 304,560]/[LCM of 206,170]= 16/17510
Therefore, the GCF of 304/206,560/170 is 16/17510.
To find the highest common factor of 304,560, we have to find the factors of both numbers and list the highest common factor.
The factors of 304 are 1, 2, 4, 8, 16, 19, 38, 76, 152, 304
The factors of 560 are 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 35, 40, 56, 70, 80, 112, 140, 280, 560
The HCF of 304,560 is 16.
Lets's calculate GCF of 304,560
| 2 | 304, 560 |
| 2 | 152, 280 |
| 2 | 76, 140 |
| 2 | 38, 70 |
| 19, 35 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 = 16
Greatest Common Factor of 304,560 By Matching Biggest Common Factor Method
Now, list down the factors of 304
:1,2,4,8,16,19,38,76,152,304
Now, list down the factors of 560
:1,2,4,5,7,8,10,14,16,20,28,35,40,56,70,80,112,140,280,560
Greatest Common Factor
We found the factors 304,560 . The biggest common factor number is the GCF number.
So the greatest common factor 304,560 is 16.
Lets's calculate LCM of 206,170
| 2 | 206, 170 |
| 103, 85 |
∴ So the LCM of the given numbers is 2 x 103 x 85 = 17510
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 16/17510
Therefore, the GCF of Fractions 304/206,560/170 is 16/17510
Least Common Multiple of 206,170 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 206,170 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(206,170) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(206,170) x common factors =2 x 1 = 2
LCM(206,170) = ( 206 × 170 ) / 2
LCM(206,170) = 35020 / 2
LCM(206,170) = 17510
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FAQs on GCF of Fractions of 304/206, 560/170
1. What is the HCF of 304,560?
The HCF of 304,560 is 16
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 304/206, 560/170?
Answer: GCF of Numerators as per given numbers 304/206, 560/170 is
GCF of Numerators i.e. for 304,560 is 16
LCM of denominators i.e. for 206,170 is 17510.
Thus, GCF of Fractions is 16/17510.Finally, GCF of Fractions for 304/206, 560/170 is 16/17510.