GCF of 136/33, 289/7205
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 136/33, 289/7205 i.e 17/21615 easily. The following is the detailed procedure to determine the greatest common factor of fractions 136/33, 289/7205.
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 136/33,289/7205?
Given fractions are 136/33,289/7205
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 136/33,289/7205, numerators are 136,289
Denominators are 33,7205
The GCF of 136,289 is 17 .
LCM of 33,7205 is 21615.
The greatest common factor of 136/33,289/7205 = [GCF of 136,289]/[LCM of 33,7205]= 17/21615
Therefore, the GCF of 136/33,289/7205 is 17/21615.
To find the highest common factor of 136,289, we have to find the factors of both numbers and list the highest common factor.
The factors of 136 are 1, 2, 4, 8, 17, 34, 68, 136
The factors of 289 are 1, 17, 289
The HCF of 136,289 is 17.
Lets's calculate GCF of 136,289
| 17 | 136, 289 |
| 8, 17 |
∴ So the GCF of the given numbers is 17 = 17
Greatest Common Factor of 136,289 By Matching Biggest Common Factor Method
Now, list down the factors of 136
:1,2,4,8,17,34,68,136
Now, list down the factors of 289
:1,17,289
Greatest Common Factor
We found the factors 136,289 . The biggest common factor number is the GCF number.
So the greatest common factor 136,289 is 17.
Lets's calculate LCM of 33,7205
| 11 | 33, 7205 |
| 3, 655 |
∴ So the LCM of the given numbers is 11 x 3 x 655 = 21615
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 17/21615
Therefore, the GCF of Fractions 136/33,289/7205 is 17/21615
Least Common Multiple of 33,7205 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 33,7205 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(33,7205) = 11
common factors(in case of two or more numbers have common factors) = 1
GCF(33,7205) x common factors =11 x 1 = 11
LCM(33,7205) = ( 33 × 7205 ) / 11
LCM(33,7205) = 237765 / 11
LCM(33,7205) = 21615
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FAQs on GCF of Fractions of 136/33, 289/7205
1. What is the HCF of 136,289?
The HCF of 136,289 is 17
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 136/33, 289/7205?
Answer: GCF of Numerators as per given numbers 136/33, 289/7205 is
GCF of Numerators i.e. for 136,289 is 17
LCM of denominators i.e. for 33,7205 is 21615.
Thus, GCF of Fractions is 17/21615.Finally, GCF of Fractions for 136/33, 289/7205 is 17/21615.