GCF of 409/715, 220/234
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 409/715, 220/234 i.e 1/12870 easily. The following is the detailed procedure to determine the greatest common factor of fractions 409/715, 220/234.
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 409/715,220/234?
Given fractions are 409/715,220/234
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 409/715,220/234, numerators are 409,220
Denominators are 715,234
The GCF of 409,220 is 1 .
LCM of 715,234 is 12870.
The greatest common factor of 409/715,220/234 = [GCF of 409,220]/[LCM of 715,234]= 1/12870
Therefore, the GCF of 409/715,220/234 is 1/12870.
To find the highest common factor of 409,220, we have to find the factors of both numbers and list the highest common factor.
The factors of 409 are 1, 409
The factors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110, 220
The HCF of 409,220 is 1.
Lets's calculate GCF of 409,220
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 409,220 By Matching Biggest Common Factor Method
Now, list down the factors of 409
:1,409
Now, list down the factors of 220
:1,2,4,5,10,11,20,22,44,55,110,220
Greatest Common Factor
We found the factors 409,220 . The biggest common factor number is the GCF number.
So the greatest common factor 409,220 is 1.
Lets's calculate LCM of 715,234
| 13 | 715, 234 |
| 55, 18 |
∴ So the LCM of the given numbers is 13 x 55 x 18 = 12870
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/12870
Therefore, the GCF of Fractions 409/715,220/234 is 1/12870
Least Common Multiple of 715,234 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 715,234 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(715,234) = 13
common factors(in case of two or more numbers have common factors) = 1
GCF(715,234) x common factors =13 x 1 = 13
LCM(715,234) = ( 715 × 234 ) / 13
LCM(715,234) = 167310 / 13
LCM(715,234) = 12870
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FAQs on GCF of Fractions of 409/715, 220/234
1. What is the HCF of 409,220?
The HCF of 409,220 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 409/715, 220/234?
Answer: GCF of Numerators as per given numbers 409/715, 220/234 is
GCF of Numerators i.e. for 409,220 is 1
LCM of denominators i.e. for 715,234 is 12870.
Thus, GCF of Fractions is 1/12870.Finally, GCF of Fractions for 409/715, 220/234 is 1/12870.