GCF of 3729/410, 7854/1520
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 3729/410, 7854/1520 i.e 33/62320 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3729/410, 7854/1520.
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 3729/410,7854/1520?
Given fractions are 3729/410,7854/1520
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 3729/410,7854/1520, numerators are 3729,7854
Denominators are 410,1520
The GCF of 3729,7854 is 33 .
LCM of 410,1520 is 62320.
The greatest common factor of 3729/410,7854/1520 = [GCF of 3729,7854]/[LCM of 410,1520]= 33/62320
Therefore, the GCF of 3729/410,7854/1520 is 33/62320.
To find the highest common factor of 3729,7854, we have to find the factors of both numbers and list the highest common factor.
The factors of 3729 are 1, 3, 11, 33, 113, 339, 1243, 3729
The factors of 7854 are 1, 2, 3, 6, 7, 11, 14, 17, 21, 22, 33, 34, 42, 51, 66, 77, 102, 119, 154, 187, 231, 238, 357, 374, 462, 561, 714, 1122, 1309, 2618, 3927, 7854
The HCF of 3729,7854 is 33.
Lets's calculate GCF of 3729,7854
| 3 | 3729, 7854 |
| 11 | 1243, 2618 |
| 113, 238 |
∴ So the GCF of the given numbers is 3 x 11 = 33
Greatest Common Factor of 3729,7854 By Matching Biggest Common Factor Method
Now, list down the factors of 3729
:1,3,11,33,113,339,1243,3729
Now, list down the factors of 7854
:1,2,3,6,7,11,14,17,21,22,33,34,42,51,66,77,102,119,154,187,231,238,357,374,462,561,714,1122,1309,2618,3927,7854
Greatest Common Factor
We found the factors 3729,7854 . The biggest common factor number is the GCF number.
So the greatest common factor 3729,7854 is 33.
Lets's calculate LCM of 410,1520
| 2 | 410, 1520 |
| 5 | 205, 760 |
| 41, 152 |
∴ So the LCM of the given numbers is 2 x 5 x 41 x 152 = 62320
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 33/62320
Therefore, the GCF of Fractions 3729/410,7854/1520 is 33/62320
Least Common Multiple of 410,1520 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 410,1520 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(410,1520) = 10
common factors(in case of two or more numbers have common factors) = 1
GCF(410,1520) x common factors =10 x 1 = 10
LCM(410,1520) = ( 410 × 1520 ) / 10
LCM(410,1520) = 623200 / 10
LCM(410,1520) = 62320
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FAQs on GCF of Fractions of 3729/410, 7854/1520
1. What is the HCF of 3729,7854?
The HCF of 3729,7854 is 33
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 3729/410, 7854/1520?
Answer: GCF of Numerators as per given numbers 3729/410, 7854/1520 is
GCF of Numerators i.e. for 3729,7854 is 33
LCM of denominators i.e. for 410,1520 is 62320.
Thus, GCF of Fractions is 33/62320.Finally, GCF of Fractions for 3729/410, 7854/1520 is 33/62320.