GCF of 837/177, 7728/384
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 837/177, 7728/384 i.e 3/22656 easily. The following is the detailed procedure to determine the greatest common factor of fractions 837/177, 7728/384.
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 837/177,7728/384?
Given fractions are 837/177,7728/384
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 837/177,7728/384, numerators are 837,7728
Denominators are 177,384
The GCF of 837,7728 is 3 .
LCM of 177,384 is 22656.
The greatest common factor of 837/177,7728/384 = [GCF of 837,7728]/[LCM of 177,384]= 3/22656
Therefore, the GCF of 837/177,7728/384 is 3/22656.
To find the highest common factor of 837,7728, we have to find the factors of both numbers and list the highest common factor.
The factors of 837 are 1, 3, 9, 27, 31, 93, 279, 837
The factors of 7728 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 23, 24, 28, 42, 46, 48, 56, 69, 84, 92, 112, 138, 161, 168, 184, 276, 322, 336, 368, 483, 552, 644, 966, 1104, 1288, 1932, 2576, 3864, 7728
The HCF of 837,7728 is 3.
Lets's calculate GCF of 837,7728
| 3 | 837, 7728 |
| 279, 2576 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 837,7728 By Matching Biggest Common Factor Method
Now, list down the factors of 837
:1,3,9,27,31,93,279,837
Now, list down the factors of 7728
:1,2,3,4,6,7,8,12,14,16,21,23,24,28,42,46,48,56,69,84,92,112,138,161,168,184,276,322,336,368,483,552,644,966,1104,1288,1932,2576,3864,7728
Greatest Common Factor
We found the factors 837,7728 . The biggest common factor number is the GCF number.
So the greatest common factor 837,7728 is 3.
Lets's calculate LCM of 177,384
| 3 | 177, 384 |
| 59, 128 |
∴ So the LCM of the given numbers is 3 x 59 x 128 = 22656
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/22656
Therefore, the GCF of Fractions 837/177,7728/384 is 3/22656
Least Common Multiple of 177,384 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 177,384 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(177,384) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(177,384) x common factors =3 x 1 = 3
LCM(177,384) = ( 177 × 384 ) / 3
LCM(177,384) = 67968 / 3
LCM(177,384) = 22656
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FAQs on GCF of Fractions of 837/177, 7728/384
1. What is the HCF of 837,7728?
The HCF of 837,7728 is 3
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 837/177, 7728/384?
Answer: GCF of Numerators as per given numbers 837/177, 7728/384 is
GCF of Numerators i.e. for 837,7728 is 3
LCM of denominators i.e. for 177,384 is 22656.
Thus, GCF of Fractions is 3/22656.Finally, GCF of Fractions for 837/177, 7728/384 is 3/22656.