GCF of 390/419, 734/300
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 390/419, 734/300 i.e 2/125700 easily. The following is the detailed procedure to determine the greatest common factor of fractions 390/419, 734/300.
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 390/419,734/300?
Given fractions are 390/419,734/300
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 390/419,734/300, numerators are 390,734
Denominators are 419,300
The GCF of 390,734 is 2 .
LCM of 419,300 is 125700.
The greatest common factor of 390/419,734/300 = [GCF of 390,734]/[LCM of 419,300]= 2/125700
Therefore, the GCF of 390/419,734/300 is 2/125700.
To find the highest common factor of 390,734, we have to find the factors of both numbers and list the highest common factor.
The factors of 390 are 1, 2, 3, 5, 6, 10, 13, 15, 26, 30, 39, 65, 78, 130, 195, 390
The factors of 734 are 1, 2, 367, 734
The HCF of 390,734 is 2.
Lets's calculate GCF of 390,734
| 2 | 390, 734 |
| 195, 367 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 390,734 By Matching Biggest Common Factor Method
Now, list down the factors of 390
:1,2,3,5,6,10,13,15,26,30,39,65,78,130,195,390
Now, list down the factors of 734
:1,2,367,734
Greatest Common Factor
We found the factors 390,734 . The biggest common factor number is the GCF number.
So the greatest common factor 390,734 is 2.
Lets's calculate LCM of 419,300
Given numbers has no common factors except 1. So, there LCM is their product i.e 125700
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/125700
Therefore, the GCF of Fractions 390/419,734/300 is 2/125700
Least Common Multiple of 419,300 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 419,300 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(419,300) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(419,300) x common factors =1 x 1 = 1
LCM(419,300) = ( 419 × 300 ) / 1
LCM(419,300) = 125700 / 1
LCM(419,300) = 125700
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FAQs on GCF of Fractions of 390/419, 734/300
1. What is the HCF of 390,734?
The HCF of 390,734 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 390/419, 734/300?
Answer: GCF of Numerators as per given numbers 390/419, 734/300 is
GCF of Numerators i.e. for 390,734 is 2
LCM of denominators i.e. for 419,300 is 125700.
Thus, GCF of Fractions is 2/125700.Finally, GCF of Fractions for 390/419, 734/300 is 2/125700.