GCF of 3078/200, 7344/415
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 3078/200, 7344/415 i.e 54/16600 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3078/200, 7344/415.
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 3078/200,7344/415?
Given fractions are 3078/200,7344/415
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 3078/200,7344/415, numerators are 3078,7344
Denominators are 200,415
The GCF of 3078,7344 is 54 .
LCM of 200,415 is 16600.
The greatest common factor of 3078/200,7344/415 = [GCF of 3078,7344]/[LCM of 200,415]= 54/16600
Therefore, the GCF of 3078/200,7344/415 is 54/16600.
To find the highest common factor of 3078,7344, we have to find the factors of both numbers and list the highest common factor.
The factors of 3078 are 1, 2, 3, 6, 9, 18, 19, 27, 38, 54, 57, 81, 114, 162, 171, 342, 513, 1026, 1539, 3078
The factors of 7344 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 17, 18, 24, 27, 34, 36, 48, 51, 54, 68, 72, 102, 108, 136, 144, 153, 204, 216, 272, 306, 408, 432, 459, 612, 816, 918, 1224, 1836, 2448, 3672, 7344
The HCF of 3078,7344 is 54.
Lets's calculate GCF of 3078,7344
| 2 | 3078, 7344 |
| 3 | 1539, 3672 |
| 3 | 513, 1224 |
| 3 | 171, 408 |
| 57, 136 |
∴ So the GCF of the given numbers is 2 x 3 x 3 x 3 = 54
Greatest Common Factor of 3078,7344 By Matching Biggest Common Factor Method
Now, list down the factors of 3078
:1,2,3,6,9,18,19,27,38,54,57,81,114,162,171,342,513,1026,1539,3078
Now, list down the factors of 7344
:1,2,3,4,6,8,9,12,16,17,18,24,27,34,36,48,51,54,68,72,102,108,136,144,153,204,216,272,306,408,432,459,612,816,918,1224,1836,2448,3672,7344
Greatest Common Factor
We found the factors 3078,7344 . The biggest common factor number is the GCF number.
So the greatest common factor 3078,7344 is 54.
Lets's calculate LCM of 200,415
| 5 | 200, 415 |
| 40, 83 |
∴ So the LCM of the given numbers is 5 x 40 x 83 = 16600
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 54/16600
Therefore, the GCF of Fractions 3078/200,7344/415 is 54/16600
Least Common Multiple of 200,415 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 200,415 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(200,415) = 5
common factors(in case of two or more numbers have common factors) = 1
GCF(200,415) x common factors =5 x 1 = 5
LCM(200,415) = ( 200 × 415 ) / 5
LCM(200,415) = 83000 / 5
LCM(200,415) = 16600
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FAQs on GCF of Fractions of 3078/200, 7344/415
1. What is the HCF of 3078,7344?
The HCF of 3078,7344 is 54
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 3078/200, 7344/415?
Answer: GCF of Numerators as per given numbers 3078/200, 7344/415 is
GCF of Numerators i.e. for 3078,7344 is 54
LCM of denominators i.e. for 200,415 is 16600.
Thus, GCF of Fractions is 54/16600.Finally, GCF of Fractions for 3078/200, 7344/415 is 54/16600.