Use our free GCF of Fractions Calculator tool to compute the GCF of 321/966, 780/208 i.e 3/100464 easily. The following is the detailed procedure to determine the greatest common factor of fractions 321/966, 780/208.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 321/966,780/208
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 321/966,780/208, numerators are 321,780
Denominators are 966,208
The GCF of 321,780 is 3 .
LCM of 966,208 is 100464.
The greatest common factor of 321/966,780/208 = [GCF of 321,780]/[LCM of 966,208]= 3/100464
Therefore, the GCF of 321/966,780/208 is 3/100464.
To find the highest common factor of 321,780, we have to find the factors of both numbers and list the highest common factor.
The factors of 321 are 1, 3, 107, 321
The factors of 780 are 1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 20, 26, 30, 39, 52, 60, 65, 78, 130, 156, 195, 260, 390, 780
The HCF of 321,780 is 3.
Lets's calculate GCF of 321,780
3 | 321, 780 |
107, 260 |
∴ So the GCF of the given numbers is 3 = 3
Now, list down the factors of 321
:1,3,107,321
Now, list down the factors of 780
:1,2,3,4,5,6,10,12,13,15,20,26,30,39,52,60,65,78,130,156,195,260,390,780
Greatest Common Factor
We found the factors 321,780 . The biggest common factor number is the GCF number.
So the greatest common factor 321,780 is 3.
Lets's calculate LCM of 966,208
2 | 966, 208 |
483, 104 |
∴ So the LCM of the given numbers is 2 x 483 x 104 = 100464
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/100464
Therefore, the GCF of Fractions 321/966,780/208 is 3/100464
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 966,208 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(966,208) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(966,208) x common factors =2 x 1 = 2
LCM(966,208) = ( 966 × 208 ) / 2
LCM(966,208) = 200928 / 2
LCM(966,208) = 100464
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 321,780?
The HCF of 321,780 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 321/966, 780/208?
Answer: GCF of Numerators as per given numbers 321/966, 780/208 is
GCF of Numerators i.e. for 321,780 is 3
LCM of denominators i.e. for 966,208 is 100464.
Thus, GCF of Fractions is 3/100464.Finally, GCF of Fractions for 321/966, 780/208 is 3/100464.