What if $n>1$ ?

Number Theory Level 1

$\large 2! = 2\times 1= 2$ which is even.

$\large 3! = 3\times2\times1 =6$ which is even.

$\large 4! = 4\times 3\times 2 \times 1 = 24$ which is even.

Is it true that $n!$ is always even for $n >1$ ?

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

Yes No

1 solution

Nitesh Chaurasia
Aug 12, 2017

For any numbers factorial greater than 1 i.e n! is (n×(n-1)×........3×2×1) where the number ends by multiplied with 2 which makes it even .

Haha.

But $1!$ is not even, so we chose the "right" starting point.

Calvin Lin Staff - 3 years, 9 months ago