Last Digit

Number Theory Level 2

What is the last digit of $1!+2!+3!+ \cdots + n!$

for $n\geq 4$ ?

Notation: $!$ is the factorial notation. For example, $8! = 1\times2\times3\times\cdots\times8$ .

The answer is 3.

1 solution

Rajdeep Ghosh
May 17, 2017

Hint :Note that $5!=120$ $6!=720$ $7!=5040$ All the succeeding factorials have one thing in common: Their last digits. Note that all factorials after and including 5 have the last digit as 0. This happens because when you multiply $4!=24$ by 5, you get a 2 and a 5 in the prime factorization of the next factorial, resulting in a 10 in the same, further resulting in the 0 at the last digit.

Last Digit

The answer is 3.

1 solution

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