GCF of 17/21, 410/85, 204/678
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 17/21, 410/85, 204/678 i.e 1/403410 easily. The following is the detailed procedure to determine the greatest common factor of fractions 17/21, 410/85, 204/678.
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 17/21,410/85,204/678?
Given fractions are 17/21,410/85,204/678
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 17/21,410/85,204/678, numerators are 17,410,204
Denominators are 21,85,678
The GCF of 17,410,204 is 1 .
LCM of 21,85,678 is 403410.
The greatest common factor of 17/21,410/85,204/678 = [GCF of 17,410,204]/[LCM of 21,85,678]= 1/403410
Therefore, the GCF of 17/21,410/85,204/678 is 1/403410.
To find the highest common factor of 17,410,204, we have to find the factors of both numbers and list the highest common factor.
The factors of 17 are 1, 17
The factors of 410 are 1, 2, 5, 10, 41, 82, 205, 410
The factors of 204 are 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102, 204
The HCF of 17,410,204 is 1.
Lets's calculate GCF of 17,410,204
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 17,410,204 By Matching Biggest Common Factor Method
Now, list down the factors of 17
:1,17
Now, list down the factors of 410
:1,2,5,10,41,82,205,410
Now, list down the factors of 204
:1,2,3,4,6,12,17,34,51,68,102,204
Greatest Common Factor
We found the factors 17,410,204 . The biggest common factor number is the GCF number.
So the greatest common factor 17,410,204 is 1.
Lets's calculate LCM of 21,85,678
| 3 | 21, 85, 678 |
| 7, 85, 226 |
∴ So the LCM of the given numbers is 3 x 7 x 85 x 226 = 403410
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/403410
Therefore, the GCF of Fractions 17/21,410/85,204/678 is 1/403410
Least Common Multiple of 21,85,678 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 21,85,678 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(21,85,678) = 1
common factors(in case of two or more numbers have common factors) = 3
GCF(21,85,678) x common factors =1 x 3 = 3
LCM(21,85,678) = ( 21 × 85 × 678 ) / 3
LCM(21,85,678) = 1210230 / 3
LCM(21,85,678) = 403410
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FAQs on GCF of Fractions of 17/21, 410/85, 204/678
1. What is the HCF of 17,410,204?
The HCF of 17,410,204 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 17/21, 410/85, 204/678?
Answer: GCF of Numerators as per given numbers 17/21, 410/85, 204/678 is
GCF of Numerators i.e. for 17,410,204 is 1
LCM of denominators i.e. for 21,85,678 is 403410.
Thus, GCF of Fractions is 1/403410.Finally, GCF of Fractions for 17/21, 410/85, 204/678 is 1/403410.