GCF of 133/212, 2265/1688
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 133/212, 2265/1688 i.e 1/89464 easily. The following is the detailed procedure to determine the greatest common factor of fractions 133/212, 2265/1688.
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 133/212,2265/1688?
Given fractions are 133/212,2265/1688
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 133/212,2265/1688, numerators are 133,2265
Denominators are 212,1688
The GCF of 133,2265 is 1 .
LCM of 212,1688 is 89464.
The greatest common factor of 133/212,2265/1688 = [GCF of 133,2265]/[LCM of 212,1688]= 1/89464
Therefore, the GCF of 133/212,2265/1688 is 1/89464.
To find the highest common factor of 133,2265, we have to find the factors of both numbers and list the highest common factor.
The factors of 133 are 1, 7, 19, 133
The factors of 2265 are 1, 3, 5, 15, 151, 453, 755, 2265
The HCF of 133,2265 is 1.
Lets's calculate GCF of 133,2265
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 133,2265 By Matching Biggest Common Factor Method
Now, list down the factors of 133
:1,7,19,133
Now, list down the factors of 2265
:1,3,5,15,151,453,755,2265
Greatest Common Factor
We found the factors 133,2265 . The biggest common factor number is the GCF number.
So the greatest common factor 133,2265 is 1.
Lets's calculate LCM of 212,1688
| 2 | 212, 1688 |
| 2 | 106, 844 |
| 53, 422 |
∴ So the LCM of the given numbers is 2 x 2 x 53 x 422 = 89464
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/89464
Therefore, the GCF of Fractions 133/212,2265/1688 is 1/89464
Least Common Multiple of 212,1688 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 212,1688 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(212,1688) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(212,1688) x common factors =4 x 1 = 4
LCM(212,1688) = ( 212 × 1688 ) / 4
LCM(212,1688) = 357856 / 4
LCM(212,1688) = 89464
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FAQs on GCF of Fractions of 133/212, 2265/1688
1. What is the HCF of 133,2265?
The HCF of 133,2265 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 133/212, 2265/1688?
Answer: GCF of Numerators as per given numbers 133/212, 2265/1688 is
GCF of Numerators i.e. for 133,2265 is 1
LCM of denominators i.e. for 212,1688 is 89464.
Thus, GCF of Fractions is 1/89464.Finally, GCF of Fractions for 133/212, 2265/1688 is 1/89464.