GCF of 410/54, 369/4152
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 410/54, 369/4152 i.e 41/37368 easily. The following is the detailed procedure to determine the greatest common factor of fractions 410/54, 369/4152.
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 410/54,369/4152?
Given fractions are 410/54,369/4152
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 410/54,369/4152, numerators are 410,369
Denominators are 54,4152
The GCF of 410,369 is 41 .
LCM of 54,4152 is 37368.
The greatest common factor of 410/54,369/4152 = [GCF of 410,369]/[LCM of 54,4152]= 41/37368
Therefore, the GCF of 410/54,369/4152 is 41/37368.
To find the highest common factor of 410,369, we have to find the factors of both numbers and list the highest common factor.
The factors of 410 are 1, 2, 5, 10, 41, 82, 205, 410
The factors of 369 are 1, 3, 9, 41, 123, 369
The HCF of 410,369 is 41.
Lets's calculate GCF of 410,369
| 41 | 410, 369 |
| 10, 9 |
∴ So the GCF of the given numbers is 41 = 41
Greatest Common Factor of 410,369 By Matching Biggest Common Factor Method
Now, list down the factors of 410
:1,2,5,10,41,82,205,410
Now, list down the factors of 369
:1,3,9,41,123,369
Greatest Common Factor
We found the factors 410,369 . The biggest common factor number is the GCF number.
So the greatest common factor 410,369 is 41.
Lets's calculate LCM of 54,4152
| 2 | 54, 4152 |
| 3 | 27, 2076 |
| 9, 692 |
∴ So the LCM of the given numbers is 2 x 3 x 9 x 692 = 37368
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 41/37368
Therefore, the GCF of Fractions 410/54,369/4152 is 41/37368
Least Common Multiple of 54,4152 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 54,4152 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(54,4152) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(54,4152) x common factors =6 x 1 = 6
LCM(54,4152) = ( 54 × 4152 ) / 6
LCM(54,4152) = 224208 / 6
LCM(54,4152) = 37368
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FAQs on GCF of Fractions of 410/54, 369/4152
1. What is the HCF of 410,369?
The HCF of 410,369 is 41
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 410/54, 369/4152?
Answer: GCF of Numerators as per given numbers 410/54, 369/4152 is
GCF of Numerators i.e. for 410,369 is 41
LCM of denominators i.e. for 54,4152 is 37368.
Thus, GCF of Fractions is 41/37368.Finally, GCF of Fractions for 410/54, 369/4152 is 41/37368.