GCF of 160/30, 580/8517
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 160/30, 580/8517 i.e 20/85170 easily. The following is the detailed procedure to determine the greatest common factor of fractions 160/30, 580/8517.
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 160/30,580/8517?
Given fractions are 160/30,580/8517
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 160/30,580/8517, numerators are 160,580
Denominators are 30,8517
The GCF of 160,580 is 20 .
LCM of 30,8517 is 85170.
The greatest common factor of 160/30,580/8517 = [GCF of 160,580]/[LCM of 30,8517]= 20/85170
Therefore, the GCF of 160/30,580/8517 is 20/85170.
To find the highest common factor of 160,580, we have to find the factors of both numbers and list the highest common factor.
The factors of 160 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, 160
The factors of 580 are 1, 2, 4, 5, 10, 20, 29, 58, 116, 145, 290, 580
The HCF of 160,580 is 20.
Lets's calculate GCF of 160,580
| 2 | 160, 580 |
| 2 | 80, 290 |
| 5 | 40, 145 |
| 8, 29 |
∴ So the GCF of the given numbers is 2 x 2 x 5 = 20
Greatest Common Factor of 160,580 By Matching Biggest Common Factor Method
Now, list down the factors of 160
:1,2,4,5,8,10,16,20,32,40,80,160
Now, list down the factors of 580
:1,2,4,5,10,20,29,58,116,145,290,580
Greatest Common Factor
We found the factors 160,580 . The biggest common factor number is the GCF number.
So the greatest common factor 160,580 is 20.
Lets's calculate LCM of 30,8517
| 3 | 30, 8517 |
| 10, 2839 |
∴ So the LCM of the given numbers is 3 x 10 x 2839 = 85170
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 20/85170
Therefore, the GCF of Fractions 160/30,580/8517 is 20/85170
Least Common Multiple of 30,8517 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 30,8517 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(30,8517) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(30,8517) x common factors =3 x 1 = 3
LCM(30,8517) = ( 30 × 8517 ) / 3
LCM(30,8517) = 255510 / 3
LCM(30,8517) = 85170
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FAQs on GCF of Fractions of 160/30, 580/8517
1. What is the HCF of 160,580?
The HCF of 160,580 is 20
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 160/30, 580/8517?
Answer: GCF of Numerators as per given numbers 160/30, 580/8517 is
GCF of Numerators i.e. for 160,580 is 20
LCM of denominators i.e. for 30,8517 is 85170.
Thus, GCF of Fractions is 20/85170.Finally, GCF of Fractions for 160/30, 580/8517 is 20/85170.