GCF of 400/204, 6174/171
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 400/204, 6174/171 i.e 2/11628 easily. The following is the detailed procedure to determine the greatest common factor of fractions 400/204, 6174/171.
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 400/204,6174/171?
Given fractions are 400/204,6174/171
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 400/204,6174/171, numerators are 400,6174
Denominators are 204,171
The GCF of 400,6174 is 2 .
LCM of 204,171 is 11628.
The greatest common factor of 400/204,6174/171 = [GCF of 400,6174]/[LCM of 204,171]= 2/11628
Therefore, the GCF of 400/204,6174/171 is 2/11628.
To find the highest common factor of 400,6174, we have to find the factors of both numbers and list the highest common factor.
The factors of 400 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400
The factors of 6174 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 49, 63, 98, 126, 147, 294, 343, 441, 686, 882, 1029, 2058, 3087, 6174
The HCF of 400,6174 is 2.
Lets's calculate GCF of 400,6174
| 2 | 400, 6174 |
| 200, 3087 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 400,6174 By Matching Biggest Common Factor Method
Now, list down the factors of 400
:1,2,4,5,8,10,16,20,25,40,50,80,100,200,400
Now, list down the factors of 6174
:1,2,3,6,7,9,14,18,21,42,49,63,98,126,147,294,343,441,686,882,1029,2058,3087,6174
Greatest Common Factor
We found the factors 400,6174 . The biggest common factor number is the GCF number.
So the greatest common factor 400,6174 is 2.
Lets's calculate LCM of 204,171
| 3 | 204, 171 |
| 68, 57 |
∴ So the LCM of the given numbers is 3 x 68 x 57 = 11628
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/11628
Therefore, the GCF of Fractions 400/204,6174/171 is 2/11628
Least Common Multiple of 204,171 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 204,171 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(204,171) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(204,171) x common factors =3 x 1 = 3
LCM(204,171) = ( 204 × 171 ) / 3
LCM(204,171) = 34884 / 3
LCM(204,171) = 11628
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FAQs on GCF of Fractions of 400/204, 6174/171
1. What is the HCF of 400,6174?
The HCF of 400,6174 is 2
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 400/204, 6174/171?
Answer: GCF of Numerators as per given numbers 400/204, 6174/171 is
GCF of Numerators i.e. for 400,6174 is 2
LCM of denominators i.e. for 204,171 is 11628.
Thus, GCF of Fractions is 2/11628.Finally, GCF of Fractions for 400/204, 6174/171 is 2/11628.