GCF of 2340/258, 8712/1404
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2340/258, 8712/1404 i.e 36/60372 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2340/258, 8712/1404.
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 2340/258,8712/1404?
Given fractions are 2340/258,8712/1404
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 2340/258,8712/1404, numerators are 2340,8712
Denominators are 258,1404
The GCF of 2340,8712 is 36 .
LCM of 258,1404 is 60372.
The greatest common factor of 2340/258,8712/1404 = [GCF of 2340,8712]/[LCM of 258,1404]= 36/60372
Therefore, the GCF of 2340/258,8712/1404 is 36/60372.
To find the highest common factor of 2340,8712, we have to find the factors of both numbers and list the highest common factor.
The factors of 2340 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 13, 15, 18, 20, 26, 30, 36, 39, 45, 52, 60, 65, 78, 90, 117, 130, 156, 180, 195, 234, 260, 390, 468, 585, 780, 1170, 2340
The factors of 8712 are 1, 2, 3, 4, 6, 8, 9, 11, 12, 18, 22, 24, 33, 36, 44, 66, 72, 88, 99, 121, 132, 198, 242, 264, 363, 396, 484, 726, 792, 968, 1089, 1452, 2178, 2904, 4356, 8712
The HCF of 2340,8712 is 36.
Lets's calculate GCF of 2340,8712
| 2 | 2340, 8712 |
| 2 | 1170, 4356 |
| 3 | 585, 2178 |
| 3 | 195, 726 |
| 65, 242 |
∴ So the GCF of the given numbers is 2 x 2 x 3 x 3 = 36
Greatest Common Factor of 2340,8712 By Matching Biggest Common Factor Method
Now, list down the factors of 2340
:1,2,3,4,5,6,9,10,12,13,15,18,20,26,30,36,39,45,52,60,65,78,90,117,130,156,180,195,234,260,390,468,585,780,1170,2340
Now, list down the factors of 8712
:1,2,3,4,6,8,9,11,12,18,22,24,33,36,44,66,72,88,99,121,132,198,242,264,363,396,484,726,792,968,1089,1452,2178,2904,4356,8712
Greatest Common Factor
We found the factors 2340,8712 . The biggest common factor number is the GCF number.
So the greatest common factor 2340,8712 is 36.
Lets's calculate LCM of 258,1404
| 2 | 258, 1404 |
| 3 | 129, 702 |
| 43, 234 |
∴ So the LCM of the given numbers is 2 x 3 x 43 x 234 = 60372
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 36/60372
Therefore, the GCF of Fractions 2340/258,8712/1404 is 36/60372
Least Common Multiple of 258,1404 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 258,1404 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(258,1404) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(258,1404) x common factors =6 x 1 = 6
LCM(258,1404) = ( 258 × 1404 ) / 6
LCM(258,1404) = 362232 / 6
LCM(258,1404) = 60372
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FAQs on GCF of Fractions of 2340/258, 8712/1404
1. What is the HCF of 2340,8712?
The HCF of 2340,8712 is 36
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 2340/258, 8712/1404?
Answer: GCF of Numerators as per given numbers 2340/258, 8712/1404 is
GCF of Numerators i.e. for 2340,8712 is 36
LCM of denominators i.e. for 258,1404 is 60372.
Thus, GCF of Fractions is 36/60372.Finally, GCF of Fractions for 2340/258, 8712/1404 is 36/60372.