GCF of 384/234, 1504/6172
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 384/234, 1504/6172 i.e 32/722124 easily. The following is the detailed procedure to determine the greatest common factor of fractions 384/234, 1504/6172.
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 384/234,1504/6172?
Given fractions are 384/234,1504/6172
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 384/234,1504/6172, numerators are 384,1504
Denominators are 234,6172
The GCF of 384,1504 is 32 .
LCM of 234,6172 is 722124.
The greatest common factor of 384/234,1504/6172 = [GCF of 384,1504]/[LCM of 234,6172]= 32/722124
Therefore, the GCF of 384/234,1504/6172 is 32/722124.
To find the highest common factor of 384,1504, we have to find the factors of both numbers and list the highest common factor.
The factors of 384 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 384
The factors of 1504 are 1, 2, 4, 8, 16, 32, 47, 94, 188, 376, 752, 1504
The HCF of 384,1504 is 32.
Lets's calculate GCF of 384,1504
| 2 | 384, 1504 |
| 2 | 192, 752 |
| 2 | 96, 376 |
| 2 | 48, 188 |
| 2 | 24, 94 |
| 12, 47 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 x 2 = 32
Greatest Common Factor of 384,1504 By Matching Biggest Common Factor Method
Now, list down the factors of 384
:1,2,3,4,6,8,12,16,24,32,48,64,96,128,192,384
Now, list down the factors of 1504
:1,2,4,8,16,32,47,94,188,376,752,1504
Greatest Common Factor
We found the factors 384,1504 . The biggest common factor number is the GCF number.
So the greatest common factor 384,1504 is 32.
Lets's calculate LCM of 234,6172
| 2 | 234, 6172 |
| 117, 3086 |
∴ So the LCM of the given numbers is 2 x 117 x 3086 = 722124
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 32/722124
Therefore, the GCF of Fractions 384/234,1504/6172 is 32/722124
Least Common Multiple of 234,6172 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 234,6172 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(234,6172) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(234,6172) x common factors =2 x 1 = 2
LCM(234,6172) = ( 234 × 6172 ) / 2
LCM(234,6172) = 1444248 / 2
LCM(234,6172) = 722124
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FAQs on GCF of Fractions of 384/234, 1504/6172
1. What is the HCF of 384,1504?
The HCF of 384,1504 is 32
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 384/234, 1504/6172?
Answer: GCF of Numerators as per given numbers 384/234, 1504/6172 is
GCF of Numerators i.e. for 384,1504 is 32
LCM of denominators i.e. for 234,6172 is 722124.
Thus, GCF of Fractions is 32/722124.Finally, GCF of Fractions for 384/234, 1504/6172 is 32/722124.