GCF of 6/82, 88/31, 22/300, 313/410
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 6/82, 88/31, 22/300, 313/410 i.e 1/381300 easily. The following is the detailed procedure to determine the greatest common factor of fractions 6/82, 88/31, 22/300, 313/410.
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 6/82,88/31,22/300,313/410?
Given fractions are 6/82,88/31,22/300,313/410
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 6/82,88/31,22/300,313/410, numerators are 6,88,22,313
Denominators are 82,31,300,410
The GCF of 6,88,22,313 is 1 .
LCM of 82,31,300,410 is 381300.
The greatest common factor of 6/82,88/31,22/300,313/410 = [GCF of 6,88,22,313]/[LCM of 82,31,300,410]= 1/381300
Therefore, the GCF of 6/82,88/31,22/300,313/410 is 1/381300.
To find the highest common factor of 6,88,22,313, we have to find the factors of both numbers and list the highest common factor.
The factors of 6 are 1, 2, 3, 6
The factors of 88 are 1, 2, 4, 8, 11, 22, 44, 88
The factors of 22 are 1, 2, 11, 22
The factors of 313 are 1, 313
The HCF of 6,88,22,313 is 1.
Lets's calculate GCF of 6,88,22,313
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 6,88,22,313 By Matching Biggest Common Factor Method
Now, list down the factors of 6
:1,2,3,6
Now, list down the factors of 88
:1,2,4,8,11,22,44,88
Now, list down the factors of 22
:1,2,11,22
Now, list down the factors of 313
:1,313
Greatest Common Factor
We found the factors 6,88,22,313 . The biggest common factor number is the GCF number.
So the greatest common factor 6,88,22,313 is 1.
Lets's calculate LCM of 82,31,300,410
| 2 | 82, 31, 300, 410 |
| 5 | 41, 31, 150, 205 |
| 41 | 41, 31, 30, 41 |
| 1, 31, 30, 1 |
∴ So the LCM of the given numbers is 2 x 5 x 41 x 1 x 31 x 30 x 1 = 381300
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/381300
Therefore, the GCF of Fractions 6/82,88/31,22/300,313/410 is 1/381300
Least Common Multiple of 82,31,300,410 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 82,31,300,410 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(82,31,300,410) = 1
common factors(in case of two or more numbers have common factors) = 820
GCF(82,31,300,410) x common factors =1 x 820 = 820
LCM(82,31,300,410) = ( 82 × 31 × 300 × 410 ) / 820
LCM(82,31,300,410) = 312666000 / 820
LCM(82,31,300,410) = 381300
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 6/82, 88/31, 22/300, 313/410
1. What is the HCF of 6,88,22,313?
The HCF of 6,88,22,313 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 6/82, 88/31, 22/300, 313/410?
Answer: GCF of Numerators as per given numbers 6/82, 88/31, 22/300, 313/410 is
GCF of Numerators i.e. for 6,88,22,313 is 1
LCM of denominators i.e. for 82,31,300,410 is 381300.
Thus, GCF of Fractions is 1/381300.Finally, GCF of Fractions for 6/82, 88/31, 22/300, 313/410 is 1/381300.