GCF of 409/676, 361/416, 308/998
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 409/676, 361/416, 308/998 i.e 1/2698592 easily. The following is the detailed procedure to determine the greatest common factor of fractions 409/676, 361/416, 308/998.
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 409/676,361/416,308/998?
Given fractions are 409/676,361/416,308/998
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 409/676,361/416,308/998, numerators are 409,361,308
Denominators are 676,416,998
The GCF of 409,361,308 is 1 .
LCM of 676,416,998 is 2698592.
The greatest common factor of 409/676,361/416,308/998 = [GCF of 409,361,308]/[LCM of 676,416,998]= 1/2698592
Therefore, the GCF of 409/676,361/416,308/998 is 1/2698592.
To find the highest common factor of 409,361,308, 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 361 are 1, 19, 361
The factors of 308 are 1, 2, 4, 7, 11, 14, 22, 28, 44, 77, 154, 308
The HCF of 409,361,308 is 1.
Lets's calculate GCF of 409,361,308
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 409,361,308 By Matching Biggest Common Factor Method
Now, list down the factors of 409
:1,409
Now, list down the factors of 361
:1,19,361
Now, list down the factors of 308
:1,2,4,7,11,14,22,28,44,77,154,308
Greatest Common Factor
We found the factors 409,361,308 . The biggest common factor number is the GCF number.
So the greatest common factor 409,361,308 is 1.
Lets's calculate LCM of 676,416,998
| 2 | 676, 416, 998 |
| 2 | 338, 208, 499 |
| 13 | 169, 104, 499 |
| 13, 8, 499 |
∴ So the LCM of the given numbers is 2 x 2 x 13 x 13 x 8 x 499 = 2698592
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2698592
Therefore, the GCF of Fractions 409/676,361/416,308/998 is 1/2698592
Least Common Multiple of 676,416,998 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 676,416,998 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(676,416,998) = 2
common factors(in case of two or more numbers have common factors) = 52
GCF(676,416,998) x common factors =2 x 52 = 104
LCM(676,416,998) = ( 676 × 416 × 998 ) / 104
LCM(676,416,998) = 280653568 / 104
LCM(676,416,998) = 2698592
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FAQs on GCF of Fractions of 409/676, 361/416, 308/998
1. What is the HCF of 409,361,308?
The HCF of 409,361,308 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 409/676, 361/416, 308/998?
Answer: GCF of Numerators as per given numbers 409/676, 361/416, 308/998 is
GCF of Numerators i.e. for 409,361,308 is 1
LCM of denominators i.e. for 676,416,998 is 2698592.
Thus, GCF of Fractions is 1/2698592.Finally, GCF of Fractions for 409/676, 361/416, 308/998 is 1/2698592.