GCF of 321/72, 814/4062
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 321/72, 814/4062 i.e 1/48744 easily. The following is the detailed procedure to determine the greatest common factor of fractions 321/72, 814/4062.
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 321/72,814/4062?
Given fractions are 321/72,814/4062
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 321/72,814/4062, numerators are 321,814
Denominators are 72,4062
The GCF of 321,814 is 1 .
LCM of 72,4062 is 48744.
The greatest common factor of 321/72,814/4062 = [GCF of 321,814]/[LCM of 72,4062]= 1/48744
Therefore, the GCF of 321/72,814/4062 is 1/48744.
To find the highest common factor of 321,814, we have to find the factors of both numbers and list the highest common factor.
The factors of 321 are 1, 3, 107, 321
The factors of 814 are 1, 2, 11, 22, 37, 74, 407, 814
The HCF of 321,814 is 1.
Lets's calculate GCF of 321,814
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 321,814 By Matching Biggest Common Factor Method
Now, list down the factors of 321
:1,3,107,321
Now, list down the factors of 814
:1,2,11,22,37,74,407,814
Greatest Common Factor
We found the factors 321,814 . The biggest common factor number is the GCF number.
So the greatest common factor 321,814 is 1.
Lets's calculate LCM of 72,4062
| 2 | 72, 4062 |
| 3 | 36, 2031 |
| 12, 677 |
∴ So the LCM of the given numbers is 2 x 3 x 12 x 677 = 48744
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/48744
Therefore, the GCF of Fractions 321/72,814/4062 is 1/48744
Least Common Multiple of 72,4062 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 72,4062 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(72,4062) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(72,4062) x common factors =6 x 1 = 6
LCM(72,4062) = ( 72 × 4062 ) / 6
LCM(72,4062) = 292464 / 6
LCM(72,4062) = 48744
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FAQs on GCF of Fractions of 321/72, 814/4062
1. What is the HCF of 321,814?
The HCF of 321,814 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 321/72, 814/4062?
Answer: GCF of Numerators as per given numbers 321/72, 814/4062 is
GCF of Numerators i.e. for 321,814 is 1
LCM of denominators i.e. for 72,4062 is 48744.
Thus, GCF of Fractions is 1/48744.Finally, GCF of Fractions for 321/72, 814/4062 is 1/48744.