GCF of 3680/105, 8580/261
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 3680/105, 8580/261 i.e 20/9135 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3680/105, 8580/261.
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 3680/105,8580/261?
Given fractions are 3680/105,8580/261
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 3680/105,8580/261, numerators are 3680,8580
Denominators are 105,261
The GCF of 3680,8580 is 20 .
LCM of 105,261 is 9135.
The greatest common factor of 3680/105,8580/261 = [GCF of 3680,8580]/[LCM of 105,261]= 20/9135
Therefore, the GCF of 3680/105,8580/261 is 20/9135.
To find the highest common factor of 3680,8580, we have to find the factors of both numbers and list the highest common factor.
The factors of 3680 are 1, 2, 4, 5, 8, 10, 16, 20, 23, 32, 40, 46, 80, 92, 115, 160, 184, 230, 368, 460, 736, 920, 1840, 3680
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 3680,8580 is 20.
Lets's calculate GCF of 3680,8580
| 2 | 3680, 8580 |
| 2 | 1840, 4290 |
| 5 | 920, 2145 |
| 184, 429 |
∴ So the GCF of the given numbers is 2 x 2 x 5 = 20
Greatest Common Factor of 3680,8580 By Matching Biggest Common Factor Method
Now, list down the factors of 3680
:1,2,4,5,8,10,16,20,23,32,40,46,80,92,115,160,184,230,368,460,736,920,1840,3680
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 3680,8580 . The biggest common factor number is the GCF number.
So the greatest common factor 3680,8580 is 20.
Lets's calculate LCM of 105,261
| 3 | 105, 261 |
| 35, 87 |
∴ So the LCM of the given numbers is 3 x 35 x 87 = 9135
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 20/9135
Therefore, the GCF of Fractions 3680/105,8580/261 is 20/9135
Least Common Multiple of 105,261 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 105,261 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(105,261) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(105,261) x common factors =3 x 1 = 3
LCM(105,261) = ( 105 × 261 ) / 3
LCM(105,261) = 27405 / 3
LCM(105,261) = 9135
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FAQs on GCF of Fractions of 3680/105, 8580/261
1. What is the HCF of 3680,8580?
The HCF of 3680,8580 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 3680/105, 8580/261?
Answer: GCF of Numerators as per given numbers 3680/105, 8580/261 is
GCF of Numerators i.e. for 3680,8580 is 20
LCM of denominators i.e. for 105,261 is 9135.
Thus, GCF of Fractions is 20/9135.Finally, GCF of Fractions for 3680/105, 8580/261 is 20/9135.