GCF of 8580/164, 5676/1378
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8580/164, 5676/1378 i.e 132/112996 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8580/164, 5676/1378.
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 8580/164,5676/1378?
Given fractions are 8580/164,5676/1378
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 8580/164,5676/1378, numerators are 8580,5676
Denominators are 164,1378
The GCF of 8580,5676 is 132 .
LCM of 164,1378 is 112996.
The greatest common factor of 8580/164,5676/1378 = [GCF of 8580,5676]/[LCM of 164,1378]= 132/112996
Therefore, the GCF of 8580/164,5676/1378 is 132/112996.
To find the highest common factor of 8580,5676, we have to find the factors of both numbers and list the highest common factor.
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 factors of 5676 are 1, 2, 3, 4, 6, 11, 12, 22, 33, 43, 44, 66, 86, 129, 132, 172, 258, 473, 516, 946, 1419, 1892, 2838, 5676
The HCF of 8580,5676 is 132.
Lets's calculate GCF of 8580,5676
| 2 | 8580, 5676 |
| 2 | 4290, 2838 |
| 3 | 2145, 1419 |
| 11 | 715, 473 |
| 65, 43 |
∴ So the GCF of the given numbers is 2 x 2 x 3 x 11 = 132
Greatest Common Factor of 8580,5676 By Matching Biggest Common Factor Method
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
Now, list down the factors of 5676
:1,2,3,4,6,11,12,22,33,43,44,66,86,129,132,172,258,473,516,946,1419,1892,2838,5676
Greatest Common Factor
We found the factors 8580,5676 . The biggest common factor number is the GCF number.
So the greatest common factor 8580,5676 is 132.
Lets's calculate LCM of 164,1378
| 2 | 164, 1378 |
| 82, 689 |
∴ So the LCM of the given numbers is 2 x 82 x 689 = 112996
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 132/112996
Therefore, the GCF of Fractions 8580/164,5676/1378 is 132/112996
Least Common Multiple of 164,1378 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 164,1378 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(164,1378) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(164,1378) x common factors =2 x 1 = 2
LCM(164,1378) = ( 164 × 1378 ) / 2
LCM(164,1378) = 225992 / 2
LCM(164,1378) = 112996
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FAQs on GCF of Fractions of 8580/164, 5676/1378
1. What is the HCF of 8580,5676?
The HCF of 8580,5676 is 132
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 8580/164, 5676/1378?
Answer: GCF of Numerators as per given numbers 8580/164, 5676/1378 is
GCF of Numerators i.e. for 8580,5676 is 132
LCM of denominators i.e. for 164,1378 is 112996.
Thus, GCF of Fractions is 132/112996.Finally, GCF of Fractions for 8580/164, 5676/1378 is 132/112996.