GCF of 124/729, 3174/419
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 124/729, 3174/419 i.e 2/305451 easily. The following is the detailed procedure to determine the greatest common factor of fractions 124/729, 3174/419.
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 124/729,3174/419?
Given fractions are 124/729,3174/419
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 124/729,3174/419, numerators are 124,3174
Denominators are 729,419
The GCF of 124,3174 is 2 .
LCM of 729,419 is 305451.
The greatest common factor of 124/729,3174/419 = [GCF of 124,3174]/[LCM of 729,419]= 2/305451
Therefore, the GCF of 124/729,3174/419 is 2/305451.
To find the highest common factor of 124,3174, we have to find the factors of both numbers and list the highest common factor.
The factors of 124 are 1, 2, 4, 31, 62, 124
The factors of 3174 are 1, 2, 3, 6, 23, 46, 69, 138, 529, 1058, 1587, 3174
The HCF of 124,3174 is 2.
Lets's calculate GCF of 124,3174
| 2 | 124, 3174 |
| 62, 1587 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 124,3174 By Matching Biggest Common Factor Method
Now, list down the factors of 124
:1,2,4,31,62,124
Now, list down the factors of 3174
:1,2,3,6,23,46,69,138,529,1058,1587,3174
Greatest Common Factor
We found the factors 124,3174 . The biggest common factor number is the GCF number.
So the greatest common factor 124,3174 is 2.
Lets's calculate LCM of 729,419
Given numbers has no common factors except 1. So, there LCM is their product i.e 305451
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/305451
Therefore, the GCF of Fractions 124/729,3174/419 is 2/305451
Least Common Multiple of 729,419 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 729,419 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(729,419) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(729,419) x common factors =1 x 1 = 1
LCM(729,419) = ( 729 × 419 ) / 1
LCM(729,419) = 305451 / 1
LCM(729,419) = 305451
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FAQs on GCF of Fractions of 124/729, 3174/419
1. What is the HCF of 124,3174?
The HCF of 124,3174 is 2
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 124/729, 3174/419?
Answer: GCF of Numerators as per given numbers 124/729, 3174/419 is
GCF of Numerators i.e. for 124,3174 is 2
LCM of denominators i.e. for 729,419 is 305451.
Thus, GCF of Fractions is 2/305451.Finally, GCF of Fractions for 124/729, 3174/419 is 2/305451.