Use our free GCF of Fractions Calculator tool to compute the GCF of 77/21, 722/10, 292/361 i.e 1/75810 easily. The following is the detailed procedure to determine the greatest common factor of fractions 77/21, 722/10, 292/361.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 77/21,722/10,292/361
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 77/21,722/10,292/361, numerators are 77,722,292
Denominators are 21,10,361
The GCF of 77,722,292 is 1 .
LCM of 21,10,361 is 75810.
The greatest common factor of 77/21,722/10,292/361 = [GCF of 77,722,292]/[LCM of 21,10,361]= 1/75810
Therefore, the GCF of 77/21,722/10,292/361 is 1/75810.
To find the highest common factor of 77,722,292, we have to find the factors of both numbers and list the highest common factor.
The factors of 77 are 1, 7, 11, 77
The factors of 722 are 1, 2, 19, 38, 361, 722
The factors of 292 are 1, 2, 4, 73, 146, 292
The HCF of 77,722,292 is 1.
Lets's calculate GCF of 77,722,292
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 77
:1,7,11,77
Now, list down the factors of 722
:1,2,19,38,361,722
Now, list down the factors of 292
:1,2,4,73,146,292
Greatest Common Factor
We found the factors 77,722,292 . The biggest common factor number is the GCF number.
So the greatest common factor 77,722,292 is 1.
Lets's calculate LCM of 21,10,361
Given numbers has no common factors except 1. So, there LCM is their product i.e 75810
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/75810
Therefore, the GCF of Fractions 77/21,722/10,292/361 is 1/75810
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 21,10,361 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(21,10,361) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(21,10,361) x common factors =1 x 1 = 1
LCM(21,10,361) = ( 21 × 10 × 361 ) / 1
LCM(21,10,361) = 75810 / 1
LCM(21,10,361) = 75810
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 77,722,292?
The HCF of 77,722,292 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 77/21, 722/10, 292/361?
Answer: GCF of Numerators as per given numbers 77/21, 722/10, 292/361 is
GCF of Numerators i.e. for 77,722,292 is 1
LCM of denominators i.e. for 21,10,361 is 75810.
Thus, GCF of Fractions is 1/75810.Finally, GCF of Fractions for 77/21, 722/10, 292/361 is 1/75810.