Use our free GCF of Fractions Calculator tool to compute the GCF of 411/714, 504/706 i.e 3/252042 easily. The following is the detailed procedure to determine the greatest common factor of fractions 411/714, 504/706.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 411/714,504/706
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 411/714,504/706, numerators are 411,504
Denominators are 714,706
The GCF of 411,504 is 3 .
LCM of 714,706 is 252042.
The greatest common factor of 411/714,504/706 = [GCF of 411,504]/[LCM of 714,706]= 3/252042
Therefore, the GCF of 411/714,504/706 is 3/252042.
To find the highest common factor of 411,504, we have to find the factors of both numbers and list the highest common factor.
The factors of 411 are 1, 3, 137, 411
The factors of 504 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 56, 63, 72, 84, 126, 168, 252, 504
The HCF of 411,504 is 3.
Lets's calculate GCF of 411,504
3 | 411, 504 |
137, 168 |
∴ So the GCF of the given numbers is 3 = 3
Now, list down the factors of 411
:1,3,137,411
Now, list down the factors of 504
:1,2,3,4,6,7,8,9,12,14,18,21,24,28,36,42,56,63,72,84,126,168,252,504
Greatest Common Factor
We found the factors 411,504 . The biggest common factor number is the GCF number.
So the greatest common factor 411,504 is 3.
Lets's calculate LCM of 714,706
2 | 714, 706 |
357, 353 |
∴ So the LCM of the given numbers is 2 x 357 x 353 = 252042
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/252042
Therefore, the GCF of Fractions 411/714,504/706 is 3/252042
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 714,706 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(714,706) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(714,706) x common factors =2 x 1 = 2
LCM(714,706) = ( 714 × 706 ) / 2
LCM(714,706) = 504084 / 2
LCM(714,706) = 252042
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 411,504?
The HCF of 411,504 is 3
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 411/714, 504/706?
Answer: GCF of Numerators as per given numbers 411/714, 504/706 is
GCF of Numerators i.e. for 411,504 is 3
LCM of denominators i.e. for 714,706 is 252042.
Thus, GCF of Fractions is 3/252042.Finally, GCF of Fractions for 411/714, 504/706 is 3/252042.