GCF of 1302/972, 4309/5716
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1302/972, 4309/5716 i.e 31/1388988 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1302/972, 4309/5716.
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 1302/972,4309/5716?
Given fractions are 1302/972,4309/5716
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 1302/972,4309/5716, numerators are 1302,4309
Denominators are 972,5716
The GCF of 1302,4309 is 31 .
LCM of 972,5716 is 1388988.
The greatest common factor of 1302/972,4309/5716 = [GCF of 1302,4309]/[LCM of 972,5716]= 31/1388988
Therefore, the GCF of 1302/972,4309/5716 is 31/1388988.
To find the highest common factor of 1302,4309, we have to find the factors of both numbers and list the highest common factor.
The factors of 1302 are 1, 2, 3, 6, 7, 14, 21, 31, 42, 62, 93, 186, 217, 434, 651, 1302
The factors of 4309 are 1, 31, 139, 4309
The HCF of 1302,4309 is 31.
Lets's calculate GCF of 1302,4309
| 31 | 1302, 4309 |
| 42, 139 |
∴ So the GCF of the given numbers is 31 = 31
Greatest Common Factor of 1302,4309 By Matching Biggest Common Factor Method
Now, list down the factors of 1302
:1,2,3,6,7,14,21,31,42,62,93,186,217,434,651,1302
Now, list down the factors of 4309
:1,31,139,4309
Greatest Common Factor
We found the factors 1302,4309 . The biggest common factor number is the GCF number.
So the greatest common factor 1302,4309 is 31.
Lets's calculate LCM of 972,5716
| 2 | 972, 5716 |
| 2 | 486, 2858 |
| 243, 1429 |
∴ So the LCM of the given numbers is 2 x 2 x 243 x 1429 = 1388988
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 31/1388988
Therefore, the GCF of Fractions 1302/972,4309/5716 is 31/1388988
Least Common Multiple of 972,5716 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 972,5716 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(972,5716) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(972,5716) x common factors =4 x 1 = 4
LCM(972,5716) = ( 972 × 5716 ) / 4
LCM(972,5716) = 5555952 / 4
LCM(972,5716) = 1388988
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FAQs on GCF of Fractions of 1302/972, 4309/5716
1. What is the HCF of 1302,4309?
The HCF of 1302,4309 is 31
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 1302/972, 4309/5716?
Answer: GCF of Numerators as per given numbers 1302/972, 4309/5716 is
GCF of Numerators i.e. for 1302,4309 is 31
LCM of denominators i.e. for 972,5716 is 1388988.
Thus, GCF of Fractions is 31/1388988.Finally, GCF of Fractions for 1302/972, 4309/5716 is 31/1388988.