GCF of 1084/290, 7728/2170
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1084/290, 7728/2170 i.e 4/62930 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1084/290, 7728/2170.
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 1084/290,7728/2170?
Given fractions are 1084/290,7728/2170
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 1084/290,7728/2170, numerators are 1084,7728
Denominators are 290,2170
The GCF of 1084,7728 is 4 .
LCM of 290,2170 is 62930.
The greatest common factor of 1084/290,7728/2170 = [GCF of 1084,7728]/[LCM of 290,2170]= 4/62930
Therefore, the GCF of 1084/290,7728/2170 is 4/62930.
To find the highest common factor of 1084,7728, we have to find the factors of both numbers and list the highest common factor.
The factors of 1084 are 1, 2, 4, 271, 542, 1084
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 1084,7728 is 4.
Lets's calculate GCF of 1084,7728
| 2 | 1084, 7728 |
| 2 | 542, 3864 |
| 271, 1932 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Greatest Common Factor of 1084,7728 By Matching Biggest Common Factor Method
Now, list down the factors of 1084
:1,2,4,271,542,1084
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 1084,7728 . The biggest common factor number is the GCF number.
So the greatest common factor 1084,7728 is 4.
Lets's calculate LCM of 290,2170
| 2 | 290, 2170 |
| 5 | 145, 1085 |
| 29, 217 |
∴ So the LCM of the given numbers is 2 x 5 x 29 x 217 = 62930
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/62930
Therefore, the GCF of Fractions 1084/290,7728/2170 is 4/62930
Least Common Multiple of 290,2170 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 290,2170 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(290,2170) = 10
common factors(in case of two or more numbers have common factors) = 1
GCF(290,2170) x common factors =10 x 1 = 10
LCM(290,2170) = ( 290 × 2170 ) / 10
LCM(290,2170) = 629300 / 10
LCM(290,2170) = 62930
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FAQs on GCF of Fractions of 1084/290, 7728/2170
1. What is the HCF of 1084,7728?
The HCF of 1084,7728 is 4
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 1084/290, 7728/2170?
Answer: GCF of Numerators as per given numbers 1084/290, 7728/2170 is
GCF of Numerators i.e. for 1084,7728 is 4
LCM of denominators i.e. for 290,2170 is 62930.
Thus, GCF of Fractions is 4/62930.Finally, GCF of Fractions for 1084/290, 7728/2170 is 4/62930.