GCF of 1305/142, 7659/4310
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1305/142, 7659/4310 i.e 9/306010 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1305/142, 7659/4310.
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 1305/142,7659/4310?
Given fractions are 1305/142,7659/4310
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 1305/142,7659/4310, numerators are 1305,7659
Denominators are 142,4310
The GCF of 1305,7659 is 9 .
LCM of 142,4310 is 306010.
The greatest common factor of 1305/142,7659/4310 = [GCF of 1305,7659]/[LCM of 142,4310]= 9/306010
Therefore, the GCF of 1305/142,7659/4310 is 9/306010.
To find the highest common factor of 1305,7659, we have to find the factors of both numbers and list the highest common factor.
The factors of 1305 are 1, 3, 5, 9, 15, 29, 45, 87, 145, 261, 435, 1305
The factors of 7659 are 1, 3, 9, 23, 37, 69, 111, 207, 333, 851, 2553, 7659
The HCF of 1305,7659 is 9.
Lets's calculate GCF of 1305,7659
| 3 | 1305, 7659 |
| 3 | 435, 2553 |
| 145, 851 |
∴ So the GCF of the given numbers is 3 x 3 = 9
Greatest Common Factor of 1305,7659 By Matching Biggest Common Factor Method
Now, list down the factors of 1305
:1,3,5,9,15,29,45,87,145,261,435,1305
Now, list down the factors of 7659
:1,3,9,23,37,69,111,207,333,851,2553,7659
Greatest Common Factor
We found the factors 1305,7659 . The biggest common factor number is the GCF number.
So the greatest common factor 1305,7659 is 9.
Lets's calculate LCM of 142,4310
| 2 | 142, 4310 |
| 71, 2155 |
∴ So the LCM of the given numbers is 2 x 71 x 2155 = 306010
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 9/306010
Therefore, the GCF of Fractions 1305/142,7659/4310 is 9/306010
Least Common Multiple of 142,4310 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 142,4310 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(142,4310) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(142,4310) x common factors =2 x 1 = 2
LCM(142,4310) = ( 142 × 4310 ) / 2
LCM(142,4310) = 612020 / 2
LCM(142,4310) = 306010
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FAQs on GCF of Fractions of 1305/142, 7659/4310
1. What is the HCF of 1305,7659?
The HCF of 1305,7659 is 9
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 1305/142, 7659/4310?
Answer: GCF of Numerators as per given numbers 1305/142, 7659/4310 is
GCF of Numerators i.e. for 1305,7659 is 9
LCM of denominators i.e. for 142,4310 is 306010.
Thus, GCF of Fractions is 9/306010.Finally, GCF of Fractions for 1305/142, 7659/4310 is 9/306010.