GCF of 133/185, 1561/419
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 133/185, 1561/419 i.e 7/77515 easily. The following is the detailed procedure to determine the greatest common factor of fractions 133/185, 1561/419.
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 133/185,1561/419?
Given fractions are 133/185,1561/419
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 133/185,1561/419, numerators are 133,1561
Denominators are 185,419
The GCF of 133,1561 is 7 .
LCM of 185,419 is 77515.
The greatest common factor of 133/185,1561/419 = [GCF of 133,1561]/[LCM of 185,419]= 7/77515
Therefore, the GCF of 133/185,1561/419 is 7/77515.
To find the highest common factor of 133,1561, 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 1561 are 1, 7, 223, 1561
The HCF of 133,1561 is 7.
Lets's calculate GCF of 133,1561
| 7 | 133, 1561 |
| 19, 223 |
∴ So the GCF of the given numbers is 7 = 7
Greatest Common Factor of 133,1561 By Matching Biggest Common Factor Method
Now, list down the factors of 133
:1,7,19,133
Now, list down the factors of 1561
:1,7,223,1561
Greatest Common Factor
We found the factors 133,1561 . The biggest common factor number is the GCF number.
So the greatest common factor 133,1561 is 7.
Lets's calculate LCM of 185,419
Given numbers has no common factors except 1. So, there LCM is their product i.e 77515
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 7/77515
Therefore, the GCF of Fractions 133/185,1561/419 is 7/77515
Least Common Multiple of 185,419 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 185,419 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(185,419) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(185,419) x common factors =1 x 1 = 1
LCM(185,419) = ( 185 × 419 ) / 1
LCM(185,419) = 77515 / 1
LCM(185,419) = 77515
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FAQs on GCF of Fractions of 133/185, 1561/419
1. What is the HCF of 133,1561?
The HCF of 133,1561 is 7
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 133/185, 1561/419?
Answer: GCF of Numerators as per given numbers 133/185, 1561/419 is
GCF of Numerators i.e. for 133,1561 is 7
LCM of denominators i.e. for 185,419 is 77515.
Thus, GCF of Fractions is 7/77515.Finally, GCF of Fractions for 133/185, 1561/419 is 7/77515.