Would you calculate 17!

Number Theory Level 3

If $17! = \overline{355687ab8096000}$ for single digit non-negative integers $a$ and $b$ , then find the value of $a + b$ .

1 solution

Dev Sharma
Aug 21, 2015

17! must be divisible by 9 and 11.

So. a + b + 3 = 0 mod9

a - b - 2 = 0 mod11

Only case possible is a = 4 and b = 2

Thus, a + b = 6

Can you tell us how you had concluded that only numbers that is divisible are 9 and 11 ?

Syed Baqir - 5 years, 9 months ago

17! includes 11 and 9.

Dev Sharma - 5 years, 9 months ago

Do you mean 17! = 17 * 16 * .... 1! ?

Syed Baqir - 5 years, 9 months ago

@Syed Baqir – yeah!! you are right

Dev Sharma - 5 years, 9 months ago

@Dev Sharma – I was wondering of other numbers that could also be divisible, do you know the way to be sure to limit and ignore other possibilities.

Syed Baqir - 5 years, 9 months ago

@Syed Baqir – I choose 9 and 11 because of their divisibility rule

Dev Sharma - 5 years, 9 months ago

@Syed Baqir – I think the number 2 also satisfies the condition

Syed Baqir - 5 years, 9 months ago

Did the same....

Aditya Kumar - 5 years ago