GCF of 3400/715, 3240/7009
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 3400/715, 3240/7009 i.e 40/5011435 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3400/715, 3240/7009.
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 3400/715,3240/7009?
Given fractions are 3400/715,3240/7009
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 3400/715,3240/7009, numerators are 3400,3240
Denominators are 715,7009
The GCF of 3400,3240 is 40 .
LCM of 715,7009 is 5011435.
The greatest common factor of 3400/715,3240/7009 = [GCF of 3400,3240]/[LCM of 715,7009]= 40/5011435
Therefore, the GCF of 3400/715,3240/7009 is 40/5011435.
To find the highest common factor of 3400,3240, we have to find the factors of both numbers and list the highest common factor.
The factors of 3400 are 1, 2, 4, 5, 8, 10, 17, 20, 25, 34, 40, 50, 68, 85, 100, 136, 170, 200, 340, 425, 680, 850, 1700, 3400
The factors of 3240 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 27, 30, 36, 40, 45, 54, 60, 72, 81, 90, 108, 120, 135, 162, 180, 216, 270, 324, 360, 405, 540, 648, 810, 1080, 1620, 3240
The HCF of 3400,3240 is 40.
Lets's calculate GCF of 3400,3240
| 2 | 3400, 3240 |
| 2 | 1700, 1620 |
| 2 | 850, 810 |
| 5 | 425, 405 |
| 85, 81 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 5 = 40
Greatest Common Factor of 3400,3240 By Matching Biggest Common Factor Method
Now, list down the factors of 3400
:1,2,4,5,8,10,17,20,25,34,40,50,68,85,100,136,170,200,340,425,680,850,1700,3400
Now, list down the factors of 3240
:1,2,3,4,5,6,8,9,10,12,15,18,20,24,27,30,36,40,45,54,60,72,81,90,108,120,135,162,180,216,270,324,360,405,540,648,810,1080,1620,3240
Greatest Common Factor
We found the factors 3400,3240 . The biggest common factor number is the GCF number.
So the greatest common factor 3400,3240 is 40.
Lets's calculate LCM of 715,7009
Given numbers has no common factors except 1. So, there LCM is their product i.e 5011435
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 40/5011435
Therefore, the GCF of Fractions 3400/715,3240/7009 is 40/5011435
Least Common Multiple of 715,7009 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 715,7009 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(715,7009) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(715,7009) x common factors =1 x 1 = 1
LCM(715,7009) = ( 715 × 7009 ) / 1
LCM(715,7009) = 5011435 / 1
LCM(715,7009) = 5011435
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FAQs on GCF of Fractions of 3400/715, 3240/7009
1. What is the HCF of 3400,3240?
The HCF of 3400,3240 is 40
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 3400/715, 3240/7009?
Answer: GCF of Numerators as per given numbers 3400/715, 3240/7009 is
GCF of Numerators i.e. for 3400,3240 is 40
LCM of denominators i.e. for 715,7009 is 5011435.
Thus, GCF of Fractions is 40/5011435.Finally, GCF of Fractions for 3400/715, 3240/7009 is 40/5011435.