GCF of 668/82, 404/30, 105/678
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 668/82, 404/30, 105/678 i.e 1/138990 easily. The following is the detailed procedure to determine the greatest common factor of fractions 668/82, 404/30, 105/678.
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 668/82,404/30,105/678?
Given fractions are 668/82,404/30,105/678
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 668/82,404/30,105/678, numerators are 668,404,105
Denominators are 82,30,678
The GCF of 668,404,105 is 1 .
LCM of 82,30,678 is 138990.
The greatest common factor of 668/82,404/30,105/678 = [GCF of 668,404,105]/[LCM of 82,30,678]= 1/138990
Therefore, the GCF of 668/82,404/30,105/678 is 1/138990.
To find the highest common factor of 668,404,105, we have to find the factors of both numbers and list the highest common factor.
The factors of 668 are 1, 2, 4, 167, 334, 668
The factors of 404 are 1, 2, 4, 101, 202, 404
The factors of 105 are 1, 3, 5, 7, 15, 21, 35, 105
The HCF of 668,404,105 is 1.
Lets's calculate GCF of 668,404,105
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 668,404,105 By Matching Biggest Common Factor Method
Now, list down the factors of 668
:1,2,4,167,334,668
Now, list down the factors of 404
:1,2,4,101,202,404
Now, list down the factors of 105
:1,3,5,7,15,21,35,105
Greatest Common Factor
We found the factors 668,404,105 . The biggest common factor number is the GCF number.
So the greatest common factor 668,404,105 is 1.
Lets's calculate LCM of 82,30,678
| 2 | 82, 30, 678 |
| 3 | 41, 15, 339 |
| 41, 5, 113 |
∴ So the LCM of the given numbers is 2 x 3 x 41 x 5 x 113 = 138990
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/138990
Therefore, the GCF of Fractions 668/82,404/30,105/678 is 1/138990
Least Common Multiple of 82,30,678 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 82,30,678 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(82,30,678) = 2
common factors(in case of two or more numbers have common factors) = 6
GCF(82,30,678) x common factors =2 x 6 = 12
LCM(82,30,678) = ( 82 × 30 × 678 ) / 12
LCM(82,30,678) = 1667880 / 12
LCM(82,30,678) = 138990
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FAQs on GCF of Fractions of 668/82, 404/30, 105/678
1. What is the HCF of 668,404,105?
The HCF of 668,404,105 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 668/82, 404/30, 105/678?
Answer: GCF of Numerators as per given numbers 668/82, 404/30, 105/678 is
GCF of Numerators i.e. for 668,404,105 is 1
LCM of denominators i.e. for 82,30,678 is 138990.
Thus, GCF of Fractions is 1/138990.Finally, GCF of Fractions for 668/82, 404/30, 105/678 is 1/138990.