Use our free GCF of Fractions Calculator tool to compute the GCF of 278/689, 946/382 i.e 2/263198 easily. The following is the detailed procedure to determine the greatest common factor of fractions 278/689, 946/382.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 278/689,946/382
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 278/689,946/382, numerators are 278,946
Denominators are 689,382
The GCF of 278,946 is 2 .
LCM of 689,382 is 263198.
The greatest common factor of 278/689,946/382 = [GCF of 278,946]/[LCM of 689,382]= 2/263198
Therefore, the GCF of 278/689,946/382 is 2/263198.
To find the highest common factor of 278,946, we have to find the factors of both numbers and list the highest common factor.
The factors of 278 are 1, 2, 139, 278
The factors of 946 are 1, 2, 11, 22, 43, 86, 473, 946
The HCF of 278,946 is 2.
Lets's calculate GCF of 278,946
2 | 278, 946 |
139, 473 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 278
:1,2,139,278
Now, list down the factors of 946
:1,2,11,22,43,86,473,946
Greatest Common Factor
We found the factors 278,946 . The biggest common factor number is the GCF number.
So the greatest common factor 278,946 is 2.
Lets's calculate LCM of 689,382
Given numbers has no common factors except 1. So, there LCM is their product i.e 263198
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/263198
Therefore, the GCF of Fractions 278/689,946/382 is 2/263198
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 689,382 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(689,382) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(689,382) x common factors =1 x 1 = 1
LCM(689,382) = ( 689 × 382 ) / 1
LCM(689,382) = 263198 / 1
LCM(689,382) = 263198
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 278,946?
The HCF of 278,946 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 278/689, 946/382?
Answer: GCF of Numerators as per given numbers 278/689, 946/382 is
GCF of Numerators i.e. for 278,946 is 2
LCM of denominators i.e. for 689,382 is 263198.
Thus, GCF of Fractions is 2/263198.Finally, GCF of Fractions for 278/689, 946/382 is 2/263198.