GCF of 407/54, 348/729
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 407/54, 348/729 i.e 1/1458 easily. The following is the detailed procedure to determine the greatest common factor of fractions 407/54, 348/729.
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 407/54,348/729?
Given fractions are 407/54,348/729
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 407/54,348/729, numerators are 407,348
Denominators are 54,729
The GCF of 407,348 is 1 .
LCM of 54,729 is 1458.
The greatest common factor of 407/54,348/729 = [GCF of 407,348]/[LCM of 54,729]= 1/1458
Therefore, the GCF of 407/54,348/729 is 1/1458.
To find the highest common factor of 407,348, we have to find the factors of both numbers and list the highest common factor.
The factors of 407 are 1, 11, 37, 407
The factors of 348 are 1, 2, 3, 4, 6, 12, 29, 58, 87, 116, 174, 348
The HCF of 407,348 is 1.
Lets's calculate GCF of 407,348
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 407,348 By Matching Biggest Common Factor Method
Now, list down the factors of 407
:1,11,37,407
Now, list down the factors of 348
:1,2,3,4,6,12,29,58,87,116,174,348
Greatest Common Factor
We found the factors 407,348 . The biggest common factor number is the GCF number.
So the greatest common factor 407,348 is 1.
Lets's calculate LCM of 54,729
| 3 | 54, 729 |
| 3 | 18, 243 |
| 3 | 6, 81 |
| 2, 27 |
∴ So the LCM of the given numbers is 3 x 3 x 3 x 2 x 27 = 1458
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1458
Therefore, the GCF of Fractions 407/54,348/729 is 1/1458
Least Common Multiple of 54,729 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 54,729 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(54,729) = 27
common factors(in case of two or more numbers have common factors) = 1
GCF(54,729) x common factors =27 x 1 = 27
LCM(54,729) = ( 54 × 729 ) / 27
LCM(54,729) = 39366 / 27
LCM(54,729) = 1458
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FAQs on GCF of Fractions of 407/54, 348/729
1. What is the HCF of 407,348?
The HCF of 407,348 is 1
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 407/54, 348/729?
Answer: GCF of Numerators as per given numbers 407/54, 348/729 is
GCF of Numerators i.e. for 407,348 is 1
LCM of denominators i.e. for 54,729 is 1458.
Thus, GCF of Fractions is 1/1458.Finally, GCF of Fractions for 407/54, 348/729 is 1/1458.