Use our free GCF of Fractions Calculator tool to compute the GCF of 352/287, 378/661 i.e 2/189707 easily. The following is the detailed procedure to determine the greatest common factor of fractions 352/287, 378/661.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 352/287,378/661
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 352/287,378/661, numerators are 352,378
Denominators are 287,661
The GCF of 352,378 is 2 .
LCM of 287,661 is 189707.
The greatest common factor of 352/287,378/661 = [GCF of 352,378]/[LCM of 287,661]= 2/189707
Therefore, the GCF of 352/287,378/661 is 2/189707.
To find the highest common factor of 352,378, we have to find the factors of both numbers and list the highest common factor.
The factors of 352 are 1, 2, 4, 8, 11, 16, 22, 32, 44, 88, 176, 352
The factors of 378 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189, 378
The HCF of 352,378 is 2.
Lets's calculate GCF of 352,378
2 | 352, 378 |
176, 189 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 352
:1,2,4,8,11,16,22,32,44,88,176,352
Now, list down the factors of 378
:1,2,3,6,7,9,14,18,21,27,42,54,63,126,189,378
Greatest Common Factor
We found the factors 352,378 . The biggest common factor number is the GCF number.
So the greatest common factor 352,378 is 2.
Lets's calculate LCM of 287,661
Given numbers has no common factors except 1. So, there LCM is their product i.e 189707
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/189707
Therefore, the GCF of Fractions 352/287,378/661 is 2/189707
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 287,661 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(287,661) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(287,661) x common factors =1 x 1 = 1
LCM(287,661) = ( 287 × 661 ) / 1
LCM(287,661) = 189707 / 1
LCM(287,661) = 189707
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 352,378?
The HCF of 352,378 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 352/287, 378/661?
Answer: GCF of Numerators as per given numbers 352/287, 378/661 is
GCF of Numerators i.e. for 352,378 is 2
LCM of denominators i.e. for 287,661 is 189707.
Thus, GCF of Fractions is 2/189707.Finally, GCF of Fractions for 352/287, 378/661 is 2/189707.