GCF of 409/686, 288/852
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 409/686, 288/852 i.e 1/292236 easily. The following is the detailed procedure to determine the greatest common factor of fractions 409/686, 288/852.
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 409/686,288/852?
Given fractions are 409/686,288/852
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 409/686,288/852, numerators are 409,288
Denominators are 686,852
The GCF of 409,288 is 1 .
LCM of 686,852 is 292236.
The greatest common factor of 409/686,288/852 = [GCF of 409,288]/[LCM of 686,852]= 1/292236
Therefore, the GCF of 409/686,288/852 is 1/292236.
To find the highest common factor of 409,288, 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 288 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 288
The HCF of 409,288 is 1.
Lets's calculate GCF of 409,288
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 409,288 By Matching Biggest Common Factor Method
Now, list down the factors of 409
:1,409
Now, list down the factors of 288
:1,2,3,4,6,8,9,12,16,18,24,32,36,48,72,96,144,288
Greatest Common Factor
We found the factors 409,288 . The biggest common factor number is the GCF number.
So the greatest common factor 409,288 is 1.
Lets's calculate LCM of 686,852
| 2 | 686, 852 |
| 343, 426 |
∴ So the LCM of the given numbers is 2 x 343 x 426 = 292236
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/292236
Therefore, the GCF of Fractions 409/686,288/852 is 1/292236
Least Common Multiple of 686,852 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 686,852 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(686,852) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(686,852) x common factors =2 x 1 = 2
LCM(686,852) = ( 686 × 852 ) / 2
LCM(686,852) = 584472 / 2
LCM(686,852) = 292236
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FAQs on GCF of Fractions of 409/686, 288/852
1. What is the HCF of 409,288?
The HCF of 409,288 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 409/686, 288/852?
Answer: GCF of Numerators as per given numbers 409/686, 288/852 is
GCF of Numerators i.e. for 409,288 is 1
LCM of denominators i.e. for 686,852 is 292236.
Thus, GCF of Fractions is 1/292236.Finally, GCF of Fractions for 409/686, 288/852 is 1/292236.