GCF of 6440/360, 8340/5709
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 6440/360, 8340/5709 i.e 20/685080 easily. The following is the detailed procedure to determine the greatest common factor of fractions 6440/360, 8340/5709.
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 6440/360,8340/5709?
Given fractions are 6440/360,8340/5709
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 6440/360,8340/5709, numerators are 6440,8340
Denominators are 360,5709
The GCF of 6440,8340 is 20 .
LCM of 360,5709 is 685080.
The greatest common factor of 6440/360,8340/5709 = [GCF of 6440,8340]/[LCM of 360,5709]= 20/685080
Therefore, the GCF of 6440/360,8340/5709 is 20/685080.
To find the highest common factor of 6440,8340, we have to find the factors of both numbers and list the highest common factor.
The factors of 6440 are 1, 2, 4, 5, 7, 8, 10, 14, 20, 23, 28, 35, 40, 46, 56, 70, 92, 115, 140, 161, 184, 230, 280, 322, 460, 644, 805, 920, 1288, 1610, 3220, 6440
The factors of 8340 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 139, 278, 417, 556, 695, 834, 1390, 1668, 2085, 2780, 4170, 8340
The HCF of 6440,8340 is 20.
Lets's calculate GCF of 6440,8340
| 2 | 6440, 8340 |
| 2 | 3220, 4170 |
| 5 | 1610, 2085 |
| 322, 417 |
∴ So the GCF of the given numbers is 2 x 2 x 5 = 20
Greatest Common Factor of 6440,8340 By Matching Biggest Common Factor Method
Now, list down the factors of 6440
:1,2,4,5,7,8,10,14,20,23,28,35,40,46,56,70,92,115,140,161,184,230,280,322,460,644,805,920,1288,1610,3220,6440
Now, list down the factors of 8340
:1,2,3,4,5,6,10,12,15,20,30,60,139,278,417,556,695,834,1390,1668,2085,2780,4170,8340
Greatest Common Factor
We found the factors 6440,8340 . The biggest common factor number is the GCF number.
So the greatest common factor 6440,8340 is 20.
Lets's calculate LCM of 360,5709
| 3 | 360, 5709 |
| 120, 1903 |
∴ So the LCM of the given numbers is 3 x 120 x 1903 = 685080
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 20/685080
Therefore, the GCF of Fractions 6440/360,8340/5709 is 20/685080
Least Common Multiple of 360,5709 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 360,5709 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(360,5709) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(360,5709) x common factors =3 x 1 = 3
LCM(360,5709) = ( 360 × 5709 ) / 3
LCM(360,5709) = 2055240 / 3
LCM(360,5709) = 685080
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 6440/360, 8340/5709
1. What is the HCF of 6440,8340?
The HCF of 6440,8340 is 20
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 6440/360, 8340/5709?
Answer: GCF of Numerators as per given numbers 6440/360, 8340/5709 is
GCF of Numerators i.e. for 6440,8340 is 20
LCM of denominators i.e. for 360,5709 is 685080.
Thus, GCF of Fractions is 20/685080.Finally, GCF of Fractions for 6440/360, 8340/5709 is 20/685080.