GCF of 1977/648, 7728/4082
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1977/648, 7728/4082 i.e 3/1322568 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1977/648, 7728/4082.
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 1977/648,7728/4082?
Given fractions are 1977/648,7728/4082
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 1977/648,7728/4082, numerators are 1977,7728
Denominators are 648,4082
The GCF of 1977,7728 is 3 .
LCM of 648,4082 is 1322568.
The greatest common factor of 1977/648,7728/4082 = [GCF of 1977,7728]/[LCM of 648,4082]= 3/1322568
Therefore, the GCF of 1977/648,7728/4082 is 3/1322568.
To find the highest common factor of 1977,7728, we have to find the factors of both numbers and list the highest common factor.
The factors of 1977 are 1, 3, 659, 1977
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 1977,7728 is 3.
Lets's calculate GCF of 1977,7728
| 3 | 1977, 7728 |
| 659, 2576 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 1977,7728 By Matching Biggest Common Factor Method
Now, list down the factors of 1977
:1,3,659,1977
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 1977,7728 . The biggest common factor number is the GCF number.
So the greatest common factor 1977,7728 is 3.
Lets's calculate LCM of 648,4082
| 2 | 648, 4082 |
| 324, 2041 |
∴ So the LCM of the given numbers is 2 x 324 x 2041 = 1322568
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/1322568
Therefore, the GCF of Fractions 1977/648,7728/4082 is 3/1322568
Least Common Multiple of 648,4082 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 648,4082 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(648,4082) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(648,4082) x common factors =2 x 1 = 2
LCM(648,4082) = ( 648 × 4082 ) / 2
LCM(648,4082) = 2645136 / 2
LCM(648,4082) = 1322568
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 1977/648, 7728/4082
1. What is the HCF of 1977,7728?
The HCF of 1977,7728 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 1977/648, 7728/4082?
Answer: GCF of Numerators as per given numbers 1977/648, 7728/4082 is
GCF of Numerators i.e. for 1977,7728 is 3
LCM of denominators i.e. for 648,4082 is 1322568.
Thus, GCF of Fractions is 3/1322568.Finally, GCF of Fractions for 1977/648, 7728/4082 is 3/1322568.