GCF of 9684/638, 9102/2174
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 9684/638, 9102/2174 i.e 6/693506 easily. The following is the detailed procedure to determine the greatest common factor of fractions 9684/638, 9102/2174.
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 9684/638,9102/2174?
Given fractions are 9684/638,9102/2174
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 9684/638,9102/2174, numerators are 9684,9102
Denominators are 638,2174
The GCF of 9684,9102 is 6 .
LCM of 638,2174 is 693506.
The greatest common factor of 9684/638,9102/2174 = [GCF of 9684,9102]/[LCM of 638,2174]= 6/693506
Therefore, the GCF of 9684/638,9102/2174 is 6/693506.
To find the highest common factor of 9684,9102, we have to find the factors of both numbers and list the highest common factor.
The factors of 9684 are 1, 2, 3, 4, 6, 9, 12, 18, 36, 269, 538, 807, 1076, 1614, 2421, 3228, 4842, 9684
The factors of 9102 are 1, 2, 3, 6, 37, 41, 74, 82, 111, 123, 222, 246, 1517, 3034, 4551, 9102
The HCF of 9684,9102 is 6.
Lets's calculate GCF of 9684,9102
| 2 | 9684, 9102 |
| 3 | 4842, 4551 |
| 1614, 1517 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Greatest Common Factor of 9684,9102 By Matching Biggest Common Factor Method
Now, list down the factors of 9684
:1,2,3,4,6,9,12,18,36,269,538,807,1076,1614,2421,3228,4842,9684
Now, list down the factors of 9102
:1,2,3,6,37,41,74,82,111,123,222,246,1517,3034,4551,9102
Greatest Common Factor
We found the factors 9684,9102 . The biggest common factor number is the GCF number.
So the greatest common factor 9684,9102 is 6.
Lets's calculate LCM of 638,2174
| 2 | 638, 2174 |
| 319, 1087 |
∴ So the LCM of the given numbers is 2 x 319 x 1087 = 693506
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/693506
Therefore, the GCF of Fractions 9684/638,9102/2174 is 6/693506
Least Common Multiple of 638,2174 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 638,2174 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(638,2174) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(638,2174) x common factors =2 x 1 = 2
LCM(638,2174) = ( 638 × 2174 ) / 2
LCM(638,2174) = 1387012 / 2
LCM(638,2174) = 693506
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 9684/638, 9102/2174
1. What is the HCF of 9684,9102?
The HCF of 9684,9102 is 6
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 9684/638, 9102/2174?
Answer: GCF of Numerators as per given numbers 9684/638, 9102/2174 is
GCF of Numerators i.e. for 9684,9102 is 6
LCM of denominators i.e. for 638,2174 is 693506.
Thus, GCF of Fractions is 6/693506.Finally, GCF of Fractions for 9684/638, 9102/2174 is 6/693506.