GCF of 757/78, 580/774
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 757/78, 580/774 i.e 1/10062 easily. The following is the detailed procedure to determine the greatest common factor of fractions 757/78, 580/774.
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 757/78,580/774?
Given fractions are 757/78,580/774
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 757/78,580/774, numerators are 757,580
Denominators are 78,774
The GCF of 757,580 is 1 .
LCM of 78,774 is 10062.
The greatest common factor of 757/78,580/774 = [GCF of 757,580]/[LCM of 78,774]= 1/10062
Therefore, the GCF of 757/78,580/774 is 1/10062.
To find the highest common factor of 757,580, we have to find the factors of both numbers and list the highest common factor.
The factors of 757 are 1, 757
The factors of 580 are 1, 2, 4, 5, 10, 20, 29, 58, 116, 145, 290, 580
The HCF of 757,580 is 1.
Lets's calculate GCF of 757,580
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 757,580 By Matching Biggest Common Factor Method
Now, list down the factors of 757
:1,757
Now, list down the factors of 580
:1,2,4,5,10,20,29,58,116,145,290,580
Greatest Common Factor
We found the factors 757,580 . The biggest common factor number is the GCF number.
So the greatest common factor 757,580 is 1.
Lets's calculate LCM of 78,774
| 2 | 78, 774 |
| 3 | 39, 387 |
| 13, 129 |
∴ So the LCM of the given numbers is 2 x 3 x 13 x 129 = 10062
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/10062
Therefore, the GCF of Fractions 757/78,580/774 is 1/10062
Least Common Multiple of 78,774 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 78,774 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(78,774) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(78,774) x common factors =6 x 1 = 6
LCM(78,774) = ( 78 × 774 ) / 6
LCM(78,774) = 60372 / 6
LCM(78,774) = 10062
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 757/78, 580/774
1. What is the HCF of 757,580?
The HCF of 757,580 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 757/78, 580/774?
Answer: GCF of Numerators as per given numbers 757/78, 580/774 is
GCF of Numerators i.e. for 757,580 is 1
LCM of denominators i.e. for 78,774 is 10062.
Thus, GCF of Fractions is 1/10062.Finally, GCF of Fractions for 757/78, 580/774 is 1/10062.