Use our free GCF of Fractions Calculator tool to compute the GCF of 408/808, 432/967 i.e 24/781336 easily. The following is the detailed procedure to determine the greatest common factor of fractions 408/808, 432/967.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 408/808,432/967
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 408/808,432/967, numerators are 408,432
Denominators are 808,967
The GCF of 408,432 is 24 .
LCM of 808,967 is 781336.
The greatest common factor of 408/808,432/967 = [GCF of 408,432]/[LCM of 808,967]= 24/781336
Therefore, the GCF of 408/808,432/967 is 24/781336.
To find the highest common factor of 408,432, 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 432 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 108, 144, 216, 432
The HCF of 408,432 is 24.
Lets's calculate GCF of 408,432
2 | 408, 432 |
2 | 204, 216 |
2 | 102, 108 |
3 | 51, 54 |
17, 18 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 3 = 24
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 432
:1,2,3,4,6,8,9,12,16,18,24,27,36,48,54,72,108,144,216,432
Greatest Common Factor
We found the factors 408,432 . The biggest common factor number is the GCF number.
So the greatest common factor 408,432 is 24.
Lets's calculate LCM of 808,967
Given numbers has no common factors except 1. So, there LCM is their product i.e 781336
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 24/781336
Therefore, the GCF of Fractions 408/808,432/967 is 24/781336
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 808,967 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(808,967) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(808,967) x common factors =1 x 1 = 1
LCM(808,967) = ( 808 × 967 ) / 1
LCM(808,967) = 781336 / 1
LCM(808,967) = 781336
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 408,432?
The HCF of 408,432 is 24
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 408/808, 432/967?
Answer: GCF of Numerators as per given numbers 408/808, 432/967 is
GCF of Numerators i.e. for 408,432 is 24
LCM of denominators i.e. for 808,967 is 781336.
Thus, GCF of Fractions is 24/781336.Finally, GCF of Fractions for 408/808, 432/967 is 24/781336.