Use our free GCF of Fractions Calculator tool to compute the GCF of 86/152, 786/248, 420/468 i.e 2/551304 easily. The following is the detailed procedure to determine the greatest common factor of fractions 86/152, 786/248, 420/468.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 86/152,786/248,420/468
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 86/152,786/248,420/468, numerators are 86,786,420
Denominators are 152,248,468
The GCF of 86,786,420 is 2 .
LCM of 152,248,468 is 551304.
The greatest common factor of 86/152,786/248,420/468 = [GCF of 86,786,420]/[LCM of 152,248,468]= 2/551304
Therefore, the GCF of 86/152,786/248,420/468 is 2/551304.
To find the highest common factor of 86,786,420, we have to find the factors of both numbers and list the highest common factor.
The factors of 86 are 1, 2, 43, 86
The factors of 786 are 1, 2, 3, 6, 131, 262, 393, 786
The factors of 420 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420
The HCF of 86,786,420 is 2.
Lets's calculate GCF of 86,786,420
2 | 86, 786, 420 |
43, 393, 210 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 86
:1,2,43,86
Now, list down the factors of 786
:1,2,3,6,131,262,393,786
Now, list down the factors of 420
:1,2,3,4,5,6,7,10,12,14,15,20,21,28,30,35,42,60,70,84,105,140,210,420
Greatest Common Factor
We found the factors 86,786,420 . The biggest common factor number is the GCF number.
So the greatest common factor 86,786,420 is 2.
Lets's calculate LCM of 152,248,468
2 | 152, 248, 468 |
2 | 76, 124, 234 |
2 | 38, 62, 117 |
19, 31, 117 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 19 x 31 x 117 = 551304
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/551304
Therefore, the GCF of Fractions 86/152,786/248,420/468 is 2/551304
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 152,248,468 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(152,248,468) = 4
common factors(in case of two or more numbers have common factors) = 8
GCF(152,248,468) x common factors =4 x 8 = 32
LCM(152,248,468) = ( 152 × 248 × 468 ) / 32
LCM(152,248,468) = 17641728 / 32
LCM(152,248,468) = 551304
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 86,786,420?
The HCF of 86,786,420 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 86/152, 786/248, 420/468?
Answer: GCF of Numerators as per given numbers 86/152, 786/248, 420/468 is
GCF of Numerators i.e. for 86,786,420 is 2
LCM of denominators i.e. for 152,248,468 is 551304.
Thus, GCF of Fractions is 2/551304.Finally, GCF of Fractions for 86/152, 786/248, 420/468 is 2/551304.