GCF of 7728/238, 9733/980
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7728/238, 9733/980 i.e 1/16660 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7728/238, 9733/980.
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 7728/238,9733/980?
Given fractions are 7728/238,9733/980
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 7728/238,9733/980, numerators are 7728,9733
Denominators are 238,980
The GCF of 7728,9733 is 1 .
LCM of 238,980 is 16660.
The greatest common factor of 7728/238,9733/980 = [GCF of 7728,9733]/[LCM of 238,980]= 1/16660
Therefore, the GCF of 7728/238,9733/980 is 1/16660.
To find the highest common factor of 7728,9733, we have to find the factors of both numbers and list the highest common factor.
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 factors of 9733 are 1, 9733
The HCF of 7728,9733 is 1.
Lets's calculate GCF of 7728,9733
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 7728,9733 By Matching Biggest Common Factor Method
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
Now, list down the factors of 9733
:1,9733
Greatest Common Factor
We found the factors 7728,9733 . The biggest common factor number is the GCF number.
So the greatest common factor 7728,9733 is 1.
Lets's calculate LCM of 238,980
| 2 | 238, 980 |
| 7 | 119, 490 |
| 17, 70 |
∴ So the LCM of the given numbers is 2 x 7 x 17 x 70 = 16660
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/16660
Therefore, the GCF of Fractions 7728/238,9733/980 is 1/16660
Least Common Multiple of 238,980 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 238,980 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(238,980) = 14
common factors(in case of two or more numbers have common factors) = 1
GCF(238,980) x common factors =14 x 1 = 14
LCM(238,980) = ( 238 × 980 ) / 14
LCM(238,980) = 233240 / 14
LCM(238,980) = 16660
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 7728/238, 9733/980
1. What is the HCF of 7728,9733?
The HCF of 7728,9733 is 1
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 7728/238, 9733/980?
Answer: GCF of Numerators as per given numbers 7728/238, 9733/980 is
GCF of Numerators i.e. for 7728,9733 is 1
LCM of denominators i.e. for 238,980 is 16660.
Thus, GCF of Fractions is 1/16660.Finally, GCF of Fractions for 7728/238, 9733/980 is 1/16660.