Use our free GCF of Fractions Calculator tool to compute the GCF of 408/745, 267/661 i.e 3/492445 easily. The following is the detailed procedure to determine the greatest common factor of fractions 408/745, 267/661.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 408/745,267/661
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 408/745,267/661, numerators are 408,267
Denominators are 745,661
The GCF of 408,267 is 3 .
LCM of 745,661 is 492445.
The greatest common factor of 408/745,267/661 = [GCF of 408,267]/[LCM of 745,661]= 3/492445
Therefore, the GCF of 408/745,267/661 is 3/492445.
To find the highest common factor of 408,267, we have to find the factors of both numbers and list the highest common factor.
The factors of 408 are 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, 408
The factors of 267 are 1, 3, 89, 267
The HCF of 408,267 is 3.
Lets's calculate GCF of 408,267
3 | 408, 267 |
136, 89 |
∴ So the GCF of the given numbers is 3 = 3
Now, list down the factors of 408
:1,2,3,4,6,8,12,17,24,34,51,68,102,136,204,408
Now, list down the factors of 267
:1,3,89,267
Greatest Common Factor
We found the factors 408,267 . The biggest common factor number is the GCF number.
So the greatest common factor 408,267 is 3.
Lets's calculate LCM of 745,661
Given numbers has no common factors except 1. So, there LCM is their product i.e 492445
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/492445
Therefore, the GCF of Fractions 408/745,267/661 is 3/492445
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 745,661 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(745,661) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(745,661) x common factors =1 x 1 = 1
LCM(745,661) = ( 745 × 661 ) / 1
LCM(745,661) = 492445 / 1
LCM(745,661) = 492445
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 408,267?
The HCF of 408,267 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 408/745, 267/661?
Answer: GCF of Numerators as per given numbers 408/745, 267/661 is
GCF of Numerators i.e. for 408,267 is 3
LCM of denominators i.e. for 745,661 is 492445.
Thus, GCF of Fractions is 3/492445.Finally, GCF of Fractions for 408/745, 267/661 is 3/492445.