GCF of 6384/317, 1617/577
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 6384/317, 1617/577 i.e 21/182909 easily. The following is the detailed procedure to determine the greatest common factor of fractions 6384/317, 1617/577.
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 6384/317,1617/577?
Given fractions are 6384/317,1617/577
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 6384/317,1617/577, numerators are 6384,1617
Denominators are 317,577
The GCF of 6384,1617 is 21 .
LCM of 317,577 is 182909.
The greatest common factor of 6384/317,1617/577 = [GCF of 6384,1617]/[LCM of 317,577]= 21/182909
Therefore, the GCF of 6384/317,1617/577 is 21/182909.
To find the highest common factor of 6384,1617, we have to find the factors of both numbers and list the highest common factor.
The factors of 6384 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 19, 21, 24, 28, 38, 42, 48, 56, 57, 76, 84, 112, 114, 133, 152, 168, 228, 266, 304, 336, 399, 456, 532, 798, 912, 1064, 1596, 2128, 3192, 6384
The factors of 1617 are 1, 3, 7, 11, 21, 33, 49, 77, 147, 231, 539, 1617
The HCF of 6384,1617 is 21.
Lets's calculate GCF of 6384,1617
| 3 | 6384, 1617 |
| 7 | 2128, 539 |
| 304, 77 |
∴ So the GCF of the given numbers is 3 x 7 = 21
Greatest Common Factor of 6384,1617 By Matching Biggest Common Factor Method
Now, list down the factors of 6384
:1,2,3,4,6,7,8,12,14,16,19,21,24,28,38,42,48,56,57,76,84,112,114,133,152,168,228,266,304,336,399,456,532,798,912,1064,1596,2128,3192,6384
Now, list down the factors of 1617
:1,3,7,11,21,33,49,77,147,231,539,1617
Greatest Common Factor
We found the factors 6384,1617 . The biggest common factor number is the GCF number.
So the greatest common factor 6384,1617 is 21.
Lets's calculate LCM of 317,577
Given numbers has no common factors except 1. So, there LCM is their product i.e 182909
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 21/182909
Therefore, the GCF of Fractions 6384/317,1617/577 is 21/182909
Least Common Multiple of 317,577 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 317,577 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(317,577) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(317,577) x common factors =1 x 1 = 1
LCM(317,577) = ( 317 × 577 ) / 1
LCM(317,577) = 182909 / 1
LCM(317,577) = 182909
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FAQs on GCF of Fractions of 6384/317, 1617/577
1. What is the HCF of 6384,1617?
The HCF of 6384,1617 is 21
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 6384/317, 1617/577?
Answer: GCF of Numerators as per given numbers 6384/317, 1617/577 is
GCF of Numerators i.e. for 6384,1617 is 21
LCM of denominators i.e. for 317,577 is 182909.
Thus, GCF of Fractions is 21/182909.Finally, GCF of Fractions for 6384/317, 1617/577 is 21/182909.