GCF of 390/84, 728/1647
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 390/84, 728/1647 i.e 26/46116 easily. The following is the detailed procedure to determine the greatest common factor of fractions 390/84, 728/1647.
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 390/84,728/1647?
Given fractions are 390/84,728/1647
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 390/84,728/1647, numerators are 390,728
Denominators are 84,1647
The GCF of 390,728 is 26 .
LCM of 84,1647 is 46116.
The greatest common factor of 390/84,728/1647 = [GCF of 390,728]/[LCM of 84,1647]= 26/46116
Therefore, the GCF of 390/84,728/1647 is 26/46116.
To find the highest common factor of 390,728, we have to find the factors of both numbers and list the highest common factor.
The factors of 390 are 1, 2, 3, 5, 6, 10, 13, 15, 26, 30, 39, 65, 78, 130, 195, 390
The factors of 728 are 1, 2, 4, 7, 8, 13, 14, 26, 28, 52, 56, 91, 104, 182, 364, 728
The HCF of 390,728 is 26.
Lets's calculate GCF of 390,728
| 2 | 390, 728 |
| 13 | 195, 364 |
| 15, 28 |
∴ So the GCF of the given numbers is 2 x 13 = 26
Greatest Common Factor of 390,728 By Matching Biggest Common Factor Method
Now, list down the factors of 390
:1,2,3,5,6,10,13,15,26,30,39,65,78,130,195,390
Now, list down the factors of 728
:1,2,4,7,8,13,14,26,28,52,56,91,104,182,364,728
Greatest Common Factor
We found the factors 390,728 . The biggest common factor number is the GCF number.
So the greatest common factor 390,728 is 26.
Lets's calculate LCM of 84,1647
| 3 | 84, 1647 |
| 28, 549 |
∴ So the LCM of the given numbers is 3 x 28 x 549 = 46116
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 26/46116
Therefore, the GCF of Fractions 390/84,728/1647 is 26/46116
Least Common Multiple of 84,1647 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 84,1647 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(84,1647) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(84,1647) x common factors =3 x 1 = 3
LCM(84,1647) = ( 84 × 1647 ) / 3
LCM(84,1647) = 138348 / 3
LCM(84,1647) = 46116
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FAQs on GCF of Fractions of 390/84, 728/1647
1. What is the HCF of 390,728?
The HCF of 390,728 is 26
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 390/84, 728/1647?
Answer: GCF of Numerators as per given numbers 390/84, 728/1647 is
GCF of Numerators i.e. for 390,728 is 26
LCM of denominators i.e. for 84,1647 is 46116.
Thus, GCF of Fractions is 26/46116.Finally, GCF of Fractions for 390/84, 728/1647 is 26/46116.