GCF of 2184/198, 7707/521
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2184/198, 7707/521 i.e 21/103158 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2184/198, 7707/521.
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 2184/198,7707/521?
Given fractions are 2184/198,7707/521
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 2184/198,7707/521, numerators are 2184,7707
Denominators are 198,521
The GCF of 2184,7707 is 21 .
LCM of 198,521 is 103158.
The greatest common factor of 2184/198,7707/521 = [GCF of 2184,7707]/[LCM of 198,521]= 21/103158
Therefore, the GCF of 2184/198,7707/521 is 21/103158.
To find the highest common factor of 2184,7707, we have to find the factors of both numbers and list the highest common factor.
The factors of 2184 are 1, 2, 3, 4, 6, 7, 8, 12, 13, 14, 21, 24, 26, 28, 39, 42, 52, 56, 78, 84, 91, 104, 156, 168, 182, 273, 312, 364, 546, 728, 1092, 2184
The factors of 7707 are 1, 3, 7, 21, 367, 1101, 2569, 7707
The HCF of 2184,7707 is 21.
Lets's calculate GCF of 2184,7707
| 3 | 2184, 7707 |
| 7 | 728, 2569 |
| 104, 367 |
∴ So the GCF of the given numbers is 3 x 7 = 21
Greatest Common Factor of 2184,7707 By Matching Biggest Common Factor Method
Now, list down the factors of 2184
:1,2,3,4,6,7,8,12,13,14,21,24,26,28,39,42,52,56,78,84,91,104,156,168,182,273,312,364,546,728,1092,2184
Now, list down the factors of 7707
:1,3,7,21,367,1101,2569,7707
Greatest Common Factor
We found the factors 2184,7707 . The biggest common factor number is the GCF number.
So the greatest common factor 2184,7707 is 21.
Lets's calculate LCM of 198,521
Given numbers has no common factors except 1. So, there LCM is their product i.e 103158
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 21/103158
Therefore, the GCF of Fractions 2184/198,7707/521 is 21/103158
Least Common Multiple of 198,521 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 198,521 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(198,521) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(198,521) x common factors =1 x 1 = 1
LCM(198,521) = ( 198 × 521 ) / 1
LCM(198,521) = 103158 / 1
LCM(198,521) = 103158
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 2184/198, 7707/521
1. What is the HCF of 2184,7707?
The HCF of 2184,7707 is 21
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 2184/198, 7707/521?
Answer: GCF of Numerators as per given numbers 2184/198, 7707/521 is
GCF of Numerators i.e. for 2184,7707 is 21
LCM of denominators i.e. for 198,521 is 103158.
Thus, GCF of Fractions is 21/103158.Finally, GCF of Fractions for 2184/198, 7707/521 is 21/103158.