GCF of 409/470, 6675/776
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 409/470, 6675/776 i.e 1/182360 easily. The following is the detailed procedure to determine the greatest common factor of fractions 409/470, 6675/776.
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 409/470,6675/776?
Given fractions are 409/470,6675/776
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 409/470,6675/776, numerators are 409,6675
Denominators are 470,776
The GCF of 409,6675 is 1 .
LCM of 470,776 is 182360.
The greatest common factor of 409/470,6675/776 = [GCF of 409,6675]/[LCM of 470,776]= 1/182360
Therefore, the GCF of 409/470,6675/776 is 1/182360.
To find the highest common factor of 409,6675, 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 6675 are 1, 3, 5, 15, 25, 75, 89, 267, 445, 1335, 2225, 6675
The HCF of 409,6675 is 1.
Lets's calculate GCF of 409,6675
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 409,6675 By Matching Biggest Common Factor Method
Now, list down the factors of 409
:1,409
Now, list down the factors of 6675
:1,3,5,15,25,75,89,267,445,1335,2225,6675
Greatest Common Factor
We found the factors 409,6675 . The biggest common factor number is the GCF number.
So the greatest common factor 409,6675 is 1.
Lets's calculate LCM of 470,776
| 2 | 470, 776 |
| 235, 388 |
∴ So the LCM of the given numbers is 2 x 235 x 388 = 182360
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/182360
Therefore, the GCF of Fractions 409/470,6675/776 is 1/182360
Least Common Multiple of 470,776 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 470,776 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(470,776) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(470,776) x common factors =2 x 1 = 2
LCM(470,776) = ( 470 × 776 ) / 2
LCM(470,776) = 364720 / 2
LCM(470,776) = 182360
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FAQs on GCF of Fractions of 409/470, 6675/776
1. What is the HCF of 409,6675?
The HCF of 409,6675 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 409/470, 6675/776?
Answer: GCF of Numerators as per given numbers 409/470, 6675/776 is
GCF of Numerators i.e. for 409,6675 is 1
LCM of denominators i.e. for 470,776 is 182360.
Thus, GCF of Fractions is 1/182360.Finally, GCF of Fractions for 409/470, 6675/776 is 1/182360.