# (4-digit number)*(6-digit number) equals a factorial

• K Sengupta
In summary, the equation (4-digit number)*(6-digit number) equals a factorial represents a mathematical relationship where the product of a 4-digit number and a 6-digit number is equal to the product of all positive integers up to a given number. This equation can be applied to any combination of 4-digit and 6-digit numbers, and can be solved using algebraic methods or a calculator/computer program. It has various real-world applications in fields such as mathematics, computer science, and statistics, but there is no specific strategy or shortcut for solving it. A strong understanding of algebra and factorial notation can make the solving process more efficient.
K Sengupta
Substitute each of the letters by a different decimal digit from 0 to 9 to satisfy this cryptarithmetic equation:

(ABCD)*(EFEGBH) = (EC)!

Note: None of A and E can be zero.

Last edited:
4725 * 101376 = 12!

First, let's break down the equation. We have a 4-digit number multiplied by a 6-digit number, resulting in a factorial. This means that the product of the two numbers must be a very large number, and the factorial must be equal to this product.

To solve this cryptarithmetic equation, we need to find the values for each letter (A, B, C, D, E, G, H) that satisfy the equation.

First, we know that A and E cannot be zero, as this would result in a 3-digit number when multiplied by a 4 or 6-digit number.

Next, we can start by looking at the factorial on the right side of the equation. Since the factorial is equal to the product of the two numbers, it must be a very large number. The smallest factorial that has 6 digits is 720 (6!), and the largest factorial with 6 digits is 362880 (9!).

Based on this, we can determine that E must be either 7, 8, or 9.

Now, let's look at the 4-digit number on the left side of the equation. Since A cannot be zero, it must be either 1, 2, 3, 4, 5, 6, 7, 8, or 9. This means that B, C, and D can be any number from 0 to 9.

Next, we can look at the 6-digit number on the left side of the equation. Since E is already taken and cannot be zero, G and H must be any number from 0 to 9. This means that F can be any number from 1 to 9.

Now, we have a range of numbers for each letter:

A: 1-9
B, C, D: 0-9
E: 7-9
F: 1-9
G, H: 0-9

To find a specific solution, we can start by assigning values to the letters with the most restrictions. For example, we can choose A=1, E=7, and F=1. This would give us the equation:

(1BCD)*(7G1BHG) = (7C)!

We can then start trying different combinations for the remaining letters to see if they satisfy the equation.

After some trial

## 1. What is the meaning of the equation (4-digit number)*(6-digit number) equals a factorial?

This equation represents a mathematical relationship where the product of a 4-digit number and a 6-digit number is equal to a factorial, which is the product of all positive integers from 1 up to a given number. For example, 4! (read as "four factorial") is equal to 4 x 3 x 2 x 1 = 24.

## 2. Can any 4-digit and 6-digit numbers be used in this equation?

Yes, this equation can be applied to any combination of 4-digit and 6-digit numbers. However, it is important to note that the resulting factorial will vary depending on the numbers used.

## 3. How do I solve for the missing numbers in this equation?

To solve for the missing numbers in this equation, you can use algebraic methods such as simplifying, factoring, and solving equations. Alternatively, you can also use a calculator or computer program to find the numerical value of the equation.

## 4. What real-world applications does this equation have?

This equation has various applications in fields such as mathematics, computer science, and statistics. For example, it can be used to calculate probabilities and combinations in statistics, and to solve equations and algorithms in computer science.

## 5. Is there a specific strategy or shortcut for solving this equation?

There is no specific strategy or shortcut for solving this equation, as it can be approached using different methods depending on the context and purpose. However, having a strong understanding of algebra and factorial notation can make the solving process more efficient.

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