GCF of 728/614, 6384/3673
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 728/614, 6384/3673 i.e 56/2255222 easily. The following is the detailed procedure to determine the greatest common factor of fractions 728/614, 6384/3673.
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 728/614,6384/3673?
Given fractions are 728/614,6384/3673
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 728/614,6384/3673, numerators are 728,6384
Denominators are 614,3673
The GCF of 728,6384 is 56 .
LCM of 614,3673 is 2255222.
The greatest common factor of 728/614,6384/3673 = [GCF of 728,6384]/[LCM of 614,3673]= 56/2255222
Therefore, the GCF of 728/614,6384/3673 is 56/2255222.
To find the highest common factor of 728,6384, we have to find the factors of both numbers and list the highest common factor.
The factors of 728 are 1, 2, 4, 7, 8, 13, 14, 26, 28, 52, 56, 91, 104, 182, 364, 728
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 HCF of 728,6384 is 56.
Lets's calculate GCF of 728,6384
| 2 | 728, 6384 |
| 2 | 364, 3192 |
| 2 | 182, 1596 |
| 7 | 91, 798 |
| 13, 114 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 7 = 56
Greatest Common Factor of 728,6384 By Matching Biggest Common Factor Method
Now, list down the factors of 728
:1,2,4,7,8,13,14,26,28,52,56,91,104,182,364,728
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
Greatest Common Factor
We found the factors 728,6384 . The biggest common factor number is the GCF number.
So the greatest common factor 728,6384 is 56.
Lets's calculate LCM of 614,3673
Given numbers has no common factors except 1. So, there LCM is their product i.e 2255222
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 56/2255222
Therefore, the GCF of Fractions 728/614,6384/3673 is 56/2255222
Least Common Multiple of 614,3673 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 614,3673 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(614,3673) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(614,3673) x common factors =1 x 1 = 1
LCM(614,3673) = ( 614 × 3673 ) / 1
LCM(614,3673) = 2255222 / 1
LCM(614,3673) = 2255222
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FAQs on GCF of Fractions of 728/614, 6384/3673
1. What is the HCF of 728,6384?
The HCF of 728,6384 is 56
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 728/614, 6384/3673?
Answer: GCF of Numerators as per given numbers 728/614, 6384/3673 is
GCF of Numerators i.e. for 728,6384 is 56
LCM of denominators i.e. for 614,3673 is 2255222.
Thus, GCF of Fractions is 56/2255222.Finally, GCF of Fractions for 728/614, 6384/3673 is 56/2255222.