Use our free GCF of Fractions Calculator tool to compute the GCF of 588/615, 9744/9471 i.e 84/47355 easily. The following is the detailed procedure to determine the greatest common factor of fractions 588/615, 9744/9471.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 588/615,9744/9471
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 588/615,9744/9471, numerators are 588,9744
Denominators are 615,9471
The GCF of 588,9744 is 84 .
LCM of 615,9471 is 47355.
The greatest common factor of 588/615,9744/9471 = [GCF of 588,9744]/[LCM of 615,9471]= 84/47355
Therefore, the GCF of 588/615,9744/9471 is 84/47355.
To find the highest common factor of 588,9744, we have to find the factors of both numbers and list the highest common factor.
The factors of 588 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 49, 84, 98, 147, 196, 294, 588
The factors of 9744 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 29, 42, 48, 56, 58, 84, 87, 112, 116, 168, 174, 203, 232, 336, 348, 406, 464, 609, 696, 812, 1218, 1392, 1624, 2436, 3248, 4872, 9744
The HCF of 588,9744 is 84.
Lets's calculate GCF of 588,9744
2 | 588, 9744 |
2 | 294, 4872 |
3 | 147, 2436 |
7 | 49, 812 |
7, 116 |
∴ So the GCF of the given numbers is 2 x 2 x 3 x 7 = 84
Now, list down the factors of 588
:1,2,3,4,6,7,12,14,21,28,42,49,84,98,147,196,294,588
Now, list down the factors of 9744
:1,2,3,4,6,7,8,12,14,16,21,24,28,29,42,48,56,58,84,87,112,116,168,174,203,232,336,348,406,464,609,696,812,1218,1392,1624,2436,3248,4872,9744
Greatest Common Factor
We found the factors 588,9744 . The biggest common factor number is the GCF number.
So the greatest common factor 588,9744 is 84.
Lets's calculate LCM of 615,9471
3 | 615, 9471 |
41 | 205, 3157 |
5, 77 |
∴ So the LCM of the given numbers is 3 x 41 x 5 x 77 = 47355
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 84/47355
Therefore, the GCF of Fractions 588/615,9744/9471 is 84/47355
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 615,9471 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(615,9471) = 123
common factors(in case of two or more numbers have common factors) = 1
GCF(615,9471) x common factors =123 x 1 = 123
LCM(615,9471) = ( 615 × 9471 ) / 123
LCM(615,9471) = 5824665 / 123
LCM(615,9471) = 47355
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 588,9744?
The HCF of 588,9744 is 84
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 588/615, 9744/9471?
Answer: GCF of Numerators as per given numbers 588/615, 9744/9471 is
GCF of Numerators i.e. for 588,9744 is 84
LCM of denominators i.e. for 615,9471 is 47355.
Thus, GCF of Fractions is 84/47355.Finally, GCF of Fractions for 588/615, 9744/9471 is 84/47355.