GCF of 130/528, 123/219
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 130/528, 123/219 i.e 1/38544 easily. The following is the detailed procedure to determine the greatest common factor of fractions 130/528, 123/219.
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 130/528,123/219?
Given fractions are 130/528,123/219
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 130/528,123/219, numerators are 130,123
Denominators are 528,219
The GCF of 130,123 is 1 .
LCM of 528,219 is 38544.
The greatest common factor of 130/528,123/219 = [GCF of 130,123]/[LCM of 528,219]= 1/38544
Therefore, the GCF of 130/528,123/219 is 1/38544.
To find the highest common factor of 130,123, we have to find the factors of both numbers and list the highest common factor.
The factors of 130 are 1, 2, 5, 10, 13, 26, 65, 130
The factors of 123 are 1, 3, 41, 123
The HCF of 130,123 is 1.
Lets's calculate GCF of 130,123
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 130,123 By Matching Biggest Common Factor Method
Now, list down the factors of 130
:1,2,5,10,13,26,65,130
Now, list down the factors of 123
:1,3,41,123
Greatest Common Factor
We found the factors 130,123 . The biggest common factor number is the GCF number.
So the greatest common factor 130,123 is 1.
Lets's calculate LCM of 528,219
| 3 | 528, 219 |
| 176, 73 |
∴ So the LCM of the given numbers is 3 x 176 x 73 = 38544
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/38544
Therefore, the GCF of Fractions 130/528,123/219 is 1/38544
Least Common Multiple of 528,219 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 528,219 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(528,219) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(528,219) x common factors =3 x 1 = 3
LCM(528,219) = ( 528 × 219 ) / 3
LCM(528,219) = 115632 / 3
LCM(528,219) = 38544
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FAQs on GCF of Fractions of 130/528, 123/219
1. What is the HCF of 130,123?
The HCF of 130,123 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 130/528, 123/219?
Answer: GCF of Numerators as per given numbers 130/528, 123/219 is
GCF of Numerators i.e. for 130,123 is 1
LCM of denominators i.e. for 528,219 is 38544.
Thus, GCF of Fractions is 1/38544.Finally, GCF of Fractions for 130/528, 123/219 is 1/38544.