Use our free GCF of Fractions Calculator tool to compute the GCF of 456/344, 782/231 i.e 2/79464 easily. The following is the detailed procedure to determine the greatest common factor of fractions 456/344, 782/231.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 456/344,782/231
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 456/344,782/231, numerators are 456,782
Denominators are 344,231
The GCF of 456,782 is 2 .
LCM of 344,231 is 79464.
The greatest common factor of 456/344,782/231 = [GCF of 456,782]/[LCM of 344,231]= 2/79464
Therefore, the GCF of 456/344,782/231 is 2/79464.
To find the highest common factor of 456,782, we have to find the factors of both numbers and list the highest common factor.
The factors of 456 are 1, 2, 3, 4, 6, 8, 12, 19, 24, 38, 57, 76, 114, 152, 228, 456
The factors of 782 are 1, 2, 17, 23, 34, 46, 391, 782
The HCF of 456,782 is 2.
Lets's calculate GCF of 456,782
2 | 456, 782 |
228, 391 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 456
:1,2,3,4,6,8,12,19,24,38,57,76,114,152,228,456
Now, list down the factors of 782
:1,2,17,23,34,46,391,782
Greatest Common Factor
We found the factors 456,782 . The biggest common factor number is the GCF number.
So the greatest common factor 456,782 is 2.
Lets's calculate LCM of 344,231
Given numbers has no common factors except 1. So, there LCM is their product i.e 79464
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/79464
Therefore, the GCF of Fractions 456/344,782/231 is 2/79464
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 344,231 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(344,231) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(344,231) x common factors =1 x 1 = 1
LCM(344,231) = ( 344 × 231 ) / 1
LCM(344,231) = 79464 / 1
LCM(344,231) = 79464
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 456,782?
The HCF of 456,782 is 2
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 456/344, 782/231?
Answer: GCF of Numerators as per given numbers 456/344, 782/231 is
GCF of Numerators i.e. for 456,782 is 2
LCM of denominators i.e. for 344,231 is 79464.
Thus, GCF of Fractions is 2/79464.Finally, GCF of Fractions for 456/344, 782/231 is 2/79464.