GCF of 6/75, 8/50, 5/30, 77/205
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 6/75, 8/50, 5/30, 77/205 i.e 1/6150 easily. The following is the detailed procedure to determine the greatest common factor of fractions 6/75, 8/50, 5/30, 77/205.
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 6/75,8/50,5/30,77/205?
Given fractions are 6/75,8/50,5/30,77/205
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 6/75,8/50,5/30,77/205, numerators are 6,8,5,77
Denominators are 75,50,30,205
The GCF of 6,8,5,77 is 1 .
LCM of 75,50,30,205 is 6150.
The greatest common factor of 6/75,8/50,5/30,77/205 = [GCF of 6,8,5,77]/[LCM of 75,50,30,205]= 1/6150
Therefore, the GCF of 6/75,8/50,5/30,77/205 is 1/6150.
To find the highest common factor of 6,8,5,77, 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 8 are 1, 2, 4, 8
The factors of 5 are 1, 5
The factors of 77 are 1, 7, 11, 77
The HCF of 6,8,5,77 is 1.
Lets's calculate GCF of 6,8,5,77
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 6,8,5,77 By Matching Biggest Common Factor Method
Now, list down the factors of 6
:1,2,3,6
Now, list down the factors of 8
:1,2,4,8
Now, list down the factors of 5
:1,5
Now, list down the factors of 77
:1,7,11,77
Greatest Common Factor
We found the factors 6,8,5,77 . The biggest common factor number is the GCF number.
So the greatest common factor 6,8,5,77 is 1.
Lets's calculate LCM of 75,50,30,205
| 2 | 75, 50, 30, 205 |
| 3 | 75, 25, 15, 205 |
| 5 | 25, 25, 5, 205 |
| 5 | 1, 5, 5, 41 |
| 1, 1, 1, 41 |
∴ So the LCM of the given numbers is 2 x 3 x 5 x 5 x 1 x 1 x 1 x 41 = 6150
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/6150
Therefore, the GCF of Fractions 6/75,8/50,5/30,77/205 is 1/6150
Least Common Multiple of 75,50,30,205 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 75,50,30,205 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(75,50,30,205) = 5
common factors(in case of two or more numbers have common factors) = 750
GCF(75,50,30,205) x common factors =5 x 750 = 3750
LCM(75,50,30,205) = ( 75 × 50 × 30 × 205 ) / 3750
LCM(75,50,30,205) = 23062500 / 3750
LCM(75,50,30,205) = 6150
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 6/75, 8/50, 5/30, 77/205
1. What is the HCF of 6,8,5,77?
The HCF of 6,8,5,77 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 6/75, 8/50, 5/30, 77/205?
Answer: GCF of Numerators as per given numbers 6/75, 8/50, 5/30, 77/205 is
GCF of Numerators i.e. for 6,8,5,77 is 1
LCM of denominators i.e. for 75,50,30,205 is 6150.
Thus, GCF of Fractions is 1/6150.Finally, GCF of Fractions for 6/75, 8/50, 5/30, 77/205 is 1/6150.