15! = 130*674368* * * . Insert unknown digits instead of the `*` sign.
*=7
***=000
To find the unknown digits in the expression 15!, we need to calculate the factorial of 15.
15! = 15 × 14 × 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
To simplify the calculation, we can break this down into smaller steps:
Step 1: Calculate the factorial of 10
10! = 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 3,628,800
Step 2: Calculate the factorial of 11, 12, 13, 14, and 15
11! = 11 × 10! = 11 × 3,628,800 = 39,916,800
12! = 12 × 11! = 12 × 39,916,800 = 479,001,600
13! = 13 × 12! = 13 × 479,001,600 = 6,227,020,800
14! = 14 × 13! = 14 × 6,227,020,800 = 87,178,291,200
15! = 15 × 14! = 15 × 87,178,291,200 = 1,307,674,368,000
So, the unknown digits in the expression 15! = 1,307,674,368,000 are "1,307,674,368,000".
To find the unknown digits in the expression 15! = 130*674368*, we need to calculate the factorial of 15 and determine the value of the missing digits.
The factorial of a number is the product of all positive integers up to and including that number. In this case, we are looking for 15!, which means multiplying all positive integers from 1 to 15 together.
To calculate 15! manually, you would do the following steps:
1. Start with the number 1: 1
2. Multiply by the next number, 2: 1 x 2 = 2
3. Multiply by the next number, 3: 2 x 3 = 6
4. Continue this process until you reach 15: 6 x 4 x 5 x 6 x 7 x 8 x 9 x 10 x 11 x 12 x 13 x 14 x 15
Performing this multiplication, you will find that 15! is equal to 1307674368000.
Now, let's determine the unknown digits in 130*674368*.
Since 15! is equal to 1307674368000, the missing digits can be calculated by dividing this number by the known digits. So, we have:
1307674368000 / 130 x 674368 x = 130 x 674368 x
To find the value of the missing digits, we divide both sides of the equation by 130 and 674368:
1307674368000 ÷ 130 ÷ 674368 = x
By performing this division, we find that the missing digits between 130 and 674368 are 29. Therefore, the correct expression is:
15! = 130 x 67436829 x 674368
So, the answer is 15! = 130 x 67436829 x 674368.