Factorial factor

Number Theory Level 4

Find the largest $3$ -digit prime factor of $\dbinom{2000}{1000}$

The answer is 661.

1 solution

Eddie The Head
Apr 16, 2014

$\textbf{Solution outline:-}$

Any $3$ digit prime factor that occurs in $2000!$ will also occur in $1000!$ . So we must find that prime factor that occurs at least thrice in $2000!$ .

So the factor must be close to $2000//3 = 667$ .

The prime nearest to $667$ is $661$ .

So our answer is $\boxed{661}$

I think it shouldn't be nearest, it should be the highest prime factor lower than 667

Jitesh Mittal - 7 years ago

Is there any solution for this other than consulting a list of prime numbers or a veery long sieve of Erasthotenes...?

Manuel Kahayon - 5 years, 6 months ago

Factorial factor

The answer is 661.

1 solution

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