GCF of 1638/576, 4749/6030
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1638/576, 4749/6030 i.e 3/192960 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1638/576, 4749/6030.
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 1638/576,4749/6030?
Given fractions are 1638/576,4749/6030
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 1638/576,4749/6030, numerators are 1638,4749
Denominators are 576,6030
The GCF of 1638,4749 is 3 .
LCM of 576,6030 is 192960.
The greatest common factor of 1638/576,4749/6030 = [GCF of 1638,4749]/[LCM of 576,6030]= 3/192960
Therefore, the GCF of 1638/576,4749/6030 is 3/192960.
To find the highest common factor of 1638,4749, we have to find the factors of both numbers and list the highest common factor.
The factors of 1638 are 1, 2, 3, 6, 7, 9, 13, 14, 18, 21, 26, 39, 42, 63, 78, 91, 117, 126, 182, 234, 273, 546, 819, 1638
The factors of 4749 are 1, 3, 1583, 4749
The HCF of 1638,4749 is 3.
Lets's calculate GCF of 1638,4749
| 3 | 1638, 4749 |
| 546, 1583 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 1638,4749 By Matching Biggest Common Factor Method
Now, list down the factors of 1638
:1,2,3,6,7,9,13,14,18,21,26,39,42,63,78,91,117,126,182,234,273,546,819,1638
Now, list down the factors of 4749
:1,3,1583,4749
Greatest Common Factor
We found the factors 1638,4749 . The biggest common factor number is the GCF number.
So the greatest common factor 1638,4749 is 3.
Lets's calculate LCM of 576,6030
| 2 | 576, 6030 |
| 3 | 288, 3015 |
| 3 | 96, 1005 |
| 32, 335 |
∴ So the LCM of the given numbers is 2 x 3 x 3 x 32 x 335 = 192960
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/192960
Therefore, the GCF of Fractions 1638/576,4749/6030 is 3/192960
Least Common Multiple of 576,6030 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 576,6030 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(576,6030) = 18
common factors(in case of two or more numbers have common factors) = 1
GCF(576,6030) x common factors =18 x 1 = 18
LCM(576,6030) = ( 576 × 6030 ) / 18
LCM(576,6030) = 3473280 / 18
LCM(576,6030) = 192960
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FAQs on GCF of Fractions of 1638/576, 4749/6030
1. What is the HCF of 1638,4749?
The HCF of 1638,4749 is 3
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 1638/576, 4749/6030?
Answer: GCF of Numerators as per given numbers 1638/576, 4749/6030 is
GCF of Numerators i.e. for 1638,4749 is 3
LCM of denominators i.e. for 576,6030 is 192960.
Thus, GCF of Fractions is 3/192960.Finally, GCF of Fractions for 1638/576, 4749/6030 is 3/192960.