Find A,B,C for Factorial Equation

  • MHB
  • Thread starter solakis1
  • Start date
  • Tags
    Factorial
In summary, the factorial equation is a mathematical formula used to calculate the factorial of a non-negative integer. To find the values of A, B, and C in this equation, you can use algebraic methods, a calculator, or a computer program. Any non-negative integers can be used for A, B, and C, but using negative numbers, decimals, or fractions may result in undefined or non-integer solutions. The values of A, B, and C represent the coefficients of the terms in the equation and are essential in finding the solution. There is no specific order in which you should solve the factorial equation, as long as you follow the rules of algebra and arrive at the correct solution for A, B, and C.
  • #1
solakis1
422
0
find A,B,C such that:

ABC= A!+B!+C!
 
Mathematics news on Phys.org
  • #2
hint
[sp] since 7!= 7x6x5x4x3x2x1=5040 none of the A,B,C CAN be 7,8,9 because 5040 is a 4 digit no and we are looking for a 3 digit no[/sp]
 
  • #3
Because this is a 3 digit number each digit shall be < 7 as 7! is a 4 digit number that is 5040
Now no digit can be 6 because 6! = 720 so abc >700 so aother digit becomes 7
Largest digit has be 5 because if largest digit is 4 or more we have $ABC \le 72( 3 * 4!)$
So one digit is 5
Now 5!= 120
2 digits cannot be 5 because 5! + 5! = 240 and one dgit has to be 2 and it does not satisfy.
So we have 1 digit 5 and anothee digit A = 1.
B cannot be 5 because then largest C is 4 and sum <= 145 but b =5 makes abc > 150
So C is 5 and we have 100 + 10 * B + 5 = 1 + B! + 120 $ but tying different values B = 4 so number 145
 
  • #4
kaliprasad said:
Because this is a 3 digit number each digit shall be < 7 as 7! is a 4 digit number that is 5040
Now no digit can be 6 because 6! = 720 so abc >700 so aother digit becomes 7
Largest digit has be 5 because if largest digit is 4 or more we have $ABC \le 72( 3 * 4!)$
So one digit is 5
Now 5!= 120
2 digits cannot be 5 because 5! + 5! = 240 and one dgit has to be 2 and it does not satisfy.
So we have 1 digit 5 and anothee digit A = 1.
B cannot be 5 because then largest C is 4 and sum <= 145 but b =5 makes abc > 150
So C is 5 and we have 100 + 10 * B + 5 = 1 + B! + 120 $ but tying different values B = 4 so number 145
very good but can you explicity mention which are the theorem ,definitions or axiom used to solve the above?
 
  • #5
solakis said:
very good but can you explicity mention which are the theorem ,definitions or axiom used to solve the above?
I have used the properties of factorial and positional value of numbers . other than that if you want what explicit prpoperties I have used it is nothing.
 

Related to Find A,B,C for Factorial Equation

1. What is the factorial equation?

The factorial equation is a mathematical equation used to calculate the product of a given number and all the smaller whole numbers before it. It is represented by an exclamation mark (!) after the number, for example, 5! = 5 x 4 x 3 x 2 x 1 = 120.

2. How do I find the value of A, B, and C in a factorial equation?

To find the values of A, B, and C in a factorial equation, you will need to have a system of equations with three unknowns. You can then solve for these unknowns using algebraic methods such as substitution or elimination.

3. Can I use a calculator to solve for A, B, and C in a factorial equation?

Yes, you can use a calculator to solve for A, B, and C in a factorial equation. Most scientific calculators have the ability to solve systems of equations, making it easier to find the values of these unknowns.

4. What is the significance of A, B, and C in a factorial equation?

In a factorial equation, A, B, and C represent the coefficients of the terms in the equation. These coefficients help to determine the value of the factorial equation and can also be used to find the general term in a factorial sequence.

5. Are there any real-life applications of the factorial equation?

Yes, the factorial equation has many real-life applications, such as in probability and statistics, where it is used to calculate the number of possible outcomes in a given scenario. It is also used in computer science and engineering for tasks such as data compression and encryption.

Similar threads

MHB Coefficient of Friction: Finding in a Factory
    • General Math
Replies
3
Views
1K
B Cool fact about number of digits in n!
    • General Math
Replies
3
Views
1K
MHB Positive Integer Triples $(a,b,c)$ Satisfying $a^3+b^3+c^3=(abc)^2$
    • General Math
Replies
1
Views
970
MHB Could use help, know the answers but with the process and equations
    • General Math
Replies
2
Views
2K
MHB Factorials and Exponent Challenge
    • General Math
Replies
2
Views
803
MHB What are the Positive Integer Solutions to the Factorial Equation?
    • General Math
Replies
1
Views
765
MHB Prove Simultaneous Equations: $a+b+c+d \ne 0$
    • General Math
Replies
2
Views
769
MHB Triangle Equality Proof: $\frac{a}{b}=1+\sqrt{2\left(\frac{c}{b}\right)^2-1}$
    • General Math
Replies
1
Views
809
MHB Prove Geometric Sequence with $(a,b,c)$
    • General Math
Replies
1
Views
979
MHB How to Calculate the Updated Salary Ratio in a Factory?
    • General Math
Replies
4
Views
1K

Hot Threads

Recent Insights

Back
Top