GCF of 864/31, 126/204
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 864/31, 126/204 i.e 18/6324 easily. The following is the detailed procedure to determine the greatest common factor of fractions 864/31, 126/204.
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 864/31,126/204?
Given fractions are 864/31,126/204
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 864/31,126/204, numerators are 864,126
Denominators are 31,204
The GCF of 864,126 is 18 .
LCM of 31,204 is 6324.
The greatest common factor of 864/31,126/204 = [GCF of 864,126]/[LCM of 31,204]= 18/6324
Therefore, the GCF of 864/31,126/204 is 18/6324.
To find the highest common factor of 864,126, we have to find the factors of both numbers and list the highest common factor.
The factors of 864 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 96, 108, 144, 216, 288, 432, 864
The factors of 126 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126
The HCF of 864,126 is 18.
Lets's calculate GCF of 864,126
| 2 | 864, 126 |
| 3 | 432, 63 |
| 3 | 144, 21 |
| 48, 7 |
∴ So the GCF of the given numbers is 2 x 3 x 3 = 18
Greatest Common Factor of 864,126 By Matching Biggest Common Factor Method
Now, list down the factors of 864
:1,2,3,4,6,8,9,12,16,18,24,27,32,36,48,54,72,96,108,144,216,288,432,864
Now, list down the factors of 126
:1,2,3,6,7,9,14,18,21,42,63,126
Greatest Common Factor
We found the factors 864,126 . The biggest common factor number is the GCF number.
So the greatest common factor 864,126 is 18.
Lets's calculate LCM of 31,204
Given numbers has no common factors except 1. So, there LCM is their product i.e 6324
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 18/6324
Therefore, the GCF of Fractions 864/31,126/204 is 18/6324
Least Common Multiple of 31,204 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 31,204 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(31,204) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(31,204) x common factors =1 x 1 = 1
LCM(31,204) = ( 31 × 204 ) / 1
LCM(31,204) = 6324 / 1
LCM(31,204) = 6324
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FAQs on GCF of Fractions of 864/31, 126/204
1. What is the HCF of 864,126?
The HCF of 864,126 is 18
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 864/31, 126/204?
Answer: GCF of Numerators as per given numbers 864/31, 126/204 is
GCF of Numerators i.e. for 864,126 is 18
LCM of denominators i.e. for 31,204 is 6324.
Thus, GCF of Fractions is 18/6324.Finally, GCF of Fractions for 864/31, 126/204 is 18/6324.