GCF of 9/84, 18/85, 24/909, 129/272
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 9/84, 18/85, 24/909, 129/272 i.e 3/8653680 easily. The following is the detailed procedure to determine the greatest common factor of fractions 9/84, 18/85, 24/909, 129/272.
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 9/84,18/85,24/909,129/272?
Given fractions are 9/84,18/85,24/909,129/272
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 9/84,18/85,24/909,129/272, numerators are 9,18,24,129
Denominators are 84,85,909,272
The GCF of 9,18,24,129 is 3 .
LCM of 84,85,909,272 is 8653680.
The greatest common factor of 9/84,18/85,24/909,129/272 = [GCF of 9,18,24,129]/[LCM of 84,85,909,272]= 3/8653680
Therefore, the GCF of 9/84,18/85,24/909,129/272 is 3/8653680.
To find the highest common factor of 9,18,24,129, we have to find the factors of both numbers and list the highest common factor.
The factors of 9 are 1, 3, 9
The factors of 18 are 1, 2, 3, 6, 9, 18
The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24
The factors of 129 are 1, 3, 43, 129
The HCF of 9,18,24,129 is 3.
Lets's calculate GCF of 9,18,24,129
| 3 | 9, 18, 24, 129 |
| 3, 6, 8, 43 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 9,18,24,129 By Matching Biggest Common Factor Method
Now, list down the factors of 9
:1,3,9
Now, list down the factors of 18
:1,2,3,6,9,18
Now, list down the factors of 24
:1,2,3,4,6,8,12,24
Now, list down the factors of 129
:1,3,43,129
Greatest Common Factor
We found the factors 9,18,24,129 . The biggest common factor number is the GCF number.
So the greatest common factor 9,18,24,129 is 3.
Lets's calculate LCM of 84,85,909,272
| 2 | 84, 85, 909, 272 |
| 2 | 42, 85, 909, 136 |
| 3 | 21, 85, 909, 68 |
| 17 | 7, 85, 303, 68 |
| 7, 5, 303, 4 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 17 x 7 x 5 x 303 x 4 = 8653680
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/8653680
Therefore, the GCF of Fractions 9/84,18/85,24/909,129/272 is 3/8653680
Least Common Multiple of 84,85,909,272 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 84,85,909,272 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(84,85,909,272) = 1
common factors(in case of two or more numbers have common factors) = 204
GCF(84,85,909,272) x common factors =1 x 204 = 204
LCM(84,85,909,272) = ( 84 × 85 × 909 × 272 ) / 204
LCM(84,85,909,272) = 1765350720 / 204
LCM(84,85,909,272) = 8653680
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 9/84, 18/85, 24/909, 129/272
1. What is the HCF of 9,18,24,129?
The HCF of 9,18,24,129 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 9/84, 18/85, 24/909, 129/272?
Answer: GCF of Numerators as per given numbers 9/84, 18/85, 24/909, 129/272 is
GCF of Numerators i.e. for 9,18,24,129 is 3
LCM of denominators i.e. for 84,85,909,272 is 8653680.
Thus, GCF of Fractions is 3/8653680.Finally, GCF of Fractions for 9/84, 18/85, 24/909, 129/272 is 3/8653680.