GCF of 3654/523, 6438/1016
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 3654/523, 6438/1016 i.e 174/531368 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3654/523, 6438/1016.
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 3654/523,6438/1016?
Given fractions are 3654/523,6438/1016
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 3654/523,6438/1016, numerators are 3654,6438
Denominators are 523,1016
The GCF of 3654,6438 is 174 .
LCM of 523,1016 is 531368.
The greatest common factor of 3654/523,6438/1016 = [GCF of 3654,6438]/[LCM of 523,1016]= 174/531368
Therefore, the GCF of 3654/523,6438/1016 is 174/531368.
To find the highest common factor of 3654,6438, we have to find the factors of both numbers and list the highest common factor.
The factors of 3654 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 29, 42, 58, 63, 87, 126, 174, 203, 261, 406, 522, 609, 1218, 1827, 3654
The factors of 6438 are 1, 2, 3, 6, 29, 37, 58, 74, 87, 111, 174, 222, 1073, 2146, 3219, 6438
The HCF of 3654,6438 is 174.
Lets's calculate GCF of 3654,6438
| 2 | 3654, 6438 |
| 3 | 1827, 3219 |
| 29 | 609, 1073 |
| 21, 37 |
∴ So the GCF of the given numbers is 2 x 3 x 29 = 174
Greatest Common Factor of 3654,6438 By Matching Biggest Common Factor Method
Now, list down the factors of 3654
:1,2,3,6,7,9,14,18,21,29,42,58,63,87,126,174,203,261,406,522,609,1218,1827,3654
Now, list down the factors of 6438
:1,2,3,6,29,37,58,74,87,111,174,222,1073,2146,3219,6438
Greatest Common Factor
We found the factors 3654,6438 . The biggest common factor number is the GCF number.
So the greatest common factor 3654,6438 is 174.
Lets's calculate LCM of 523,1016
Given numbers has no common factors except 1. So, there LCM is their product i.e 531368
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 174/531368
Therefore, the GCF of Fractions 3654/523,6438/1016 is 174/531368
Least Common Multiple of 523,1016 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 523,1016 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(523,1016) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(523,1016) x common factors =1 x 1 = 1
LCM(523,1016) = ( 523 × 1016 ) / 1
LCM(523,1016) = 531368 / 1
LCM(523,1016) = 531368
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 3654/523, 6438/1016
1. What is the HCF of 3654,6438?
The HCF of 3654,6438 is 174
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 3654/523, 6438/1016?
Answer: GCF of Numerators as per given numbers 3654/523, 6438/1016 is
GCF of Numerators i.e. for 3654,6438 is 174
LCM of denominators i.e. for 523,1016 is 531368.
Thus, GCF of Fractions is 174/531368.Finally, GCF of Fractions for 3654/523, 6438/1016 is 174/531368.