GCF of 20/205, 8580/7137
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 20/205, 8580/7137 i.e 20/1463085 easily. The following is the detailed procedure to determine the greatest common factor of fractions 20/205, 8580/7137.
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 20/205,8580/7137?
Given fractions are 20/205,8580/7137
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 20/205,8580/7137, numerators are 20,8580
Denominators are 205,7137
The GCF of 20,8580 is 20 .
LCM of 205,7137 is 1463085.
The greatest common factor of 20/205,8580/7137 = [GCF of 20,8580]/[LCM of 205,7137]= 20/1463085
Therefore, the GCF of 20/205,8580/7137 is 20/1463085.
To find the highest common factor of 20,8580, we have to find the factors of both numbers and list the highest common factor.
The factors of 20 are 1, 2, 4, 5, 10, 20
The factors of 8580 are 1, 2, 3, 4, 5, 6, 10, 11, 12, 13, 15, 20, 22, 26, 30, 33, 39, 44, 52, 55, 60, 65, 66, 78, 110, 130, 132, 143, 156, 165, 195, 220, 260, 286, 330, 390, 429, 572, 660, 715, 780, 858, 1430, 1716, 2145, 2860, 4290, 8580
The HCF of 20,8580 is 20.
Lets's calculate GCF of 20,8580
| 2 | 20, 8580 |
| 2 | 10, 4290 |
| 5 | 5, 2145 |
| 1, 429 |
∴ So the GCF of the given numbers is 2 x 2 x 5 = 20
Greatest Common Factor of 20,8580 By Matching Biggest Common Factor Method
Now, list down the factors of 20
:1,2,4,5,10,20
Now, list down the factors of 8580
:1,2,3,4,5,6,10,11,12,13,15,20,22,26,30,33,39,44,52,55,60,65,66,78,110,130,132,143,156,165,195,220,260,286,330,390,429,572,660,715,780,858,1430,1716,2145,2860,4290,8580
Greatest Common Factor
We found the factors 20,8580 . The biggest common factor number is the GCF number.
So the greatest common factor 20,8580 is 20.
Lets's calculate LCM of 205,7137
Given numbers has no common factors except 1. So, there LCM is their product i.e 1463085
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 20/1463085
Therefore, the GCF of Fractions 20/205,8580/7137 is 20/1463085
Least Common Multiple of 205,7137 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 205,7137 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(205,7137) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(205,7137) x common factors =1 x 1 = 1
LCM(205,7137) = ( 205 × 7137 ) / 1
LCM(205,7137) = 1463085 / 1
LCM(205,7137) = 1463085
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FAQs on GCF of Fractions of 20/205, 8580/7137
1. What is the HCF of 20,8580?
The HCF of 20,8580 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 20/205, 8580/7137?
Answer: GCF of Numerators as per given numbers 20/205, 8580/7137 is
GCF of Numerators i.e. for 20,8580 is 20
LCM of denominators i.e. for 205,7137 is 1463085.
Thus, GCF of Fractions is 20/1463085.Finally, GCF of Fractions for 20/205, 8580/7137 is 20/1463085.