Use our free GCF of Fractions Calculator tool to compute the GCF of 864/872, 658/632 i.e 2/68888 easily. The following is the detailed procedure to determine the greatest common factor of fractions 864/872, 658/632.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 864/872,658/632
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 864/872,658/632, numerators are 864,658
Denominators are 872,632
The GCF of 864,658 is 2 .
LCM of 872,632 is 68888.
The greatest common factor of 864/872,658/632 = [GCF of 864,658]/[LCM of 872,632]= 2/68888
Therefore, the GCF of 864/872,658/632 is 2/68888.
To find the highest common factor of 864,658, we have to find the factors of both numbers and list the highest common factor.
The factors of 864 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 96, 108, 144, 216, 288, 432, 864
The factors of 658 are 1, 2, 7, 14, 47, 94, 329, 658
The HCF of 864,658 is 2.
Lets's calculate GCF of 864,658
2 | 864, 658 |
432, 329 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 864
:1,2,3,4,6,8,9,12,16,18,24,27,32,36,48,54,72,96,108,144,216,288,432,864
Now, list down the factors of 658
:1,2,7,14,47,94,329,658
Greatest Common Factor
We found the factors 864,658 . The biggest common factor number is the GCF number.
So the greatest common factor 864,658 is 2.
Lets's calculate LCM of 872,632
2 | 872, 632 |
2 | 436, 316 |
2 | 218, 158 |
109, 79 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 109 x 79 = 68888
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/68888
Therefore, the GCF of Fractions 864/872,658/632 is 2/68888
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 872,632 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(872,632) = 8
common factors(in case of two or more numbers have common factors) = 1
GCF(872,632) x common factors =8 x 1 = 8
LCM(872,632) = ( 872 × 632 ) / 8
LCM(872,632) = 551104 / 8
LCM(872,632) = 68888
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 864,658?
The HCF of 864,658 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 864/872, 658/632?
Answer: GCF of Numerators as per given numbers 864/872, 658/632 is
GCF of Numerators i.e. for 864,658 is 2
LCM of denominators i.e. for 872,632 is 68888.
Thus, GCF of Fractions is 2/68888.Finally, GCF of Fractions for 864/872, 658/632 is 2/68888.