GCF of 756/31, 574/205
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 756/31, 574/205 i.e 14/6355 easily. The following is the detailed procedure to determine the greatest common factor of fractions 756/31, 574/205.
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 756/31,574/205?
Given fractions are 756/31,574/205
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 756/31,574/205, numerators are 756,574
Denominators are 31,205
The GCF of 756,574 is 14 .
LCM of 31,205 is 6355.
The greatest common factor of 756/31,574/205 = [GCF of 756,574]/[LCM of 31,205]= 14/6355
Therefore, the GCF of 756/31,574/205 is 14/6355.
To find the highest common factor of 756,574, we have to find the factors of both numbers and list the highest common factor.
The factors of 756 are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 27, 28, 36, 42, 54, 63, 84, 108, 126, 189, 252, 378, 756
The factors of 574 are 1, 2, 7, 14, 41, 82, 287, 574
The HCF of 756,574 is 14.
Lets's calculate GCF of 756,574
| 2 | 756, 574 |
| 7 | 378, 287 |
| 54, 41 |
∴ So the GCF of the given numbers is 2 x 7 = 14
Greatest Common Factor of 756,574 By Matching Biggest Common Factor Method
Now, list down the factors of 756
:1,2,3,4,6,7,9,12,14,18,21,27,28,36,42,54,63,84,108,126,189,252,378,756
Now, list down the factors of 574
:1,2,7,14,41,82,287,574
Greatest Common Factor
We found the factors 756,574 . The biggest common factor number is the GCF number.
So the greatest common factor 756,574 is 14.
Lets's calculate LCM of 31,205
Given numbers has no common factors except 1. So, there LCM is their product i.e 6355
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/6355
Therefore, the GCF of Fractions 756/31,574/205 is 14/6355
Least Common Multiple of 31,205 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 31,205 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(31,205) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(31,205) x common factors =1 x 1 = 1
LCM(31,205) = ( 31 × 205 ) / 1
LCM(31,205) = 6355 / 1
LCM(31,205) = 6355
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 756/31, 574/205
1. What is the HCF of 756,574?
The HCF of 756,574 is 14
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 756/31, 574/205?
Answer: GCF of Numerators as per given numbers 756/31, 574/205 is
GCF of Numerators i.e. for 756,574 is 14
LCM of denominators i.e. for 31,205 is 6355.
Thus, GCF of Fractions is 14/6355.Finally, GCF of Fractions for 756/31, 574/205 is 14/6355.