Use our free GCF of Fractions Calculator tool to compute the GCF of 2072/77, 8825/686 i.e 1/7546 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2072/77, 8825/686.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 2072/77,8825/686
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 2072/77,8825/686, numerators are 2072,8825
Denominators are 77,686
The GCF of 2072,8825 is 1 .
LCM of 77,686 is 7546.
The greatest common factor of 2072/77,8825/686 = [GCF of 2072,8825]/[LCM of 77,686]= 1/7546
Therefore, the GCF of 2072/77,8825/686 is 1/7546.
To find the highest common factor of 2072,8825, we have to find the factors of both numbers and list the highest common factor.
The factors of 2072 are 1, 2, 4, 7, 8, 14, 28, 37, 56, 74, 148, 259, 296, 518, 1036, 2072
The factors of 8825 are 1, 5, 25, 353, 1765, 8825
The HCF of 2072,8825 is 1.
Lets's calculate GCF of 2072,8825
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 2072
:1,2,4,7,8,14,28,37,56,74,148,259,296,518,1036,2072
Now, list down the factors of 8825
:1,5,25,353,1765,8825
Greatest Common Factor
We found the factors 2072,8825 . The biggest common factor number is the GCF number.
So the greatest common factor 2072,8825 is 1.
Lets's calculate LCM of 77,686
7 | 77, 686 |
11, 98 |
∴ So the LCM of the given numbers is 7 x 11 x 98 = 7546
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/7546
Therefore, the GCF of Fractions 2072/77,8825/686 is 1/7546
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 77,686 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(77,686) = 7
common factors(in case of two or more numbers have common factors) = 1
GCF(77,686) x common factors =7 x 1 = 7
LCM(77,686) = ( 77 × 686 ) / 7
LCM(77,686) = 52822 / 7
LCM(77,686) = 7546
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 2072,8825?
The HCF of 2072,8825 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 2072/77, 8825/686?
Answer: GCF of Numerators as per given numbers 2072/77, 8825/686 is
GCF of Numerators i.e. for 2072,8825 is 1
LCM of denominators i.e. for 77,686 is 7546.
Thus, GCF of Fractions is 1/7546.Finally, GCF of Fractions for 2072/77, 8825/686 is 1/7546.