GCF of 126/29, 189/559
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 126/29, 189/559 i.e 63/16211 easily. The following is the detailed procedure to determine the greatest common factor of fractions 126/29, 189/559.
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 126/29,189/559?
Given fractions are 126/29,189/559
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 126/29,189/559, numerators are 126,189
Denominators are 29,559
The GCF of 126,189 is 63 .
LCM of 29,559 is 16211.
The greatest common factor of 126/29,189/559 = [GCF of 126,189]/[LCM of 29,559]= 63/16211
Therefore, the GCF of 126/29,189/559 is 63/16211.
To find the highest common factor of 126,189, we have to find the factors of both numbers and list the highest common factor.
The factors of 126 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126
The factors of 189 are 1, 3, 7, 9, 21, 27, 63, 189
The HCF of 126,189 is 63.
Lets's calculate GCF of 126,189
| 3 | 126, 189 |
| 3 | 42, 63 |
| 7 | 14, 21 |
| 2, 3 |
∴ So the GCF of the given numbers is 3 x 3 x 7 = 63
Greatest Common Factor of 126,189 By Matching Biggest Common Factor Method
Now, list down the factors of 126
:1,2,3,6,7,9,14,18,21,42,63,126
Now, list down the factors of 189
:1,3,7,9,21,27,63,189
Greatest Common Factor
We found the factors 126,189 . The biggest common factor number is the GCF number.
So the greatest common factor 126,189 is 63.
Lets's calculate LCM of 29,559
Given numbers has no common factors except 1. So, there LCM is their product i.e 16211
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 63/16211
Therefore, the GCF of Fractions 126/29,189/559 is 63/16211
Least Common Multiple of 29,559 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 29,559 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(29,559) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(29,559) x common factors =1 x 1 = 1
LCM(29,559) = ( 29 × 559 ) / 1
LCM(29,559) = 16211 / 1
LCM(29,559) = 16211
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 126/29, 189/559
1. What is the HCF of 126,189?
The HCF of 126,189 is 63
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 126/29, 189/559?
Answer: GCF of Numerators as per given numbers 126/29, 189/559 is
GCF of Numerators i.e. for 126,189 is 63
LCM of denominators i.e. for 29,559 is 16211.
Thus, GCF of Fractions is 63/16211.Finally, GCF of Fractions for 126/29, 189/559 is 63/16211.