10416 has 40 divisors (see below), whose sum is σ = 31744. Its totient is φ = 2880.

The previous prime is 10399. The next prime is 10427. The reversal of 10416 is 61401.

10416 = 1² + 2² + ... + 31².

It is a Harshad number since it is a multiple of its sum of digits (12).

10416 is an undulating number in base 5.

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (5) of ones.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 321 + ... + 351.

10416 is a gapful number since it is divisible by the number (16) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 10416, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (15872).

10416 is an abundant number, since it is smaller than the sum of its proper divisors (21328).

It is a pseudoperfect number, because it is the sum of a subset of its proper divisors.

10416 is a wasteful number, since it uses less digits than its factorization.

10416 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 49 (or 43 counting only the distinct ones).

The product of its (nonzero) digits is 24, while the sum is 12.

The square root of 10416 is about 102.0588065774. The cubic root of 10416 is about 21.8390456989.

Subtracting from 10416 its sum of digits (12), we obtain a square (10404 = 102²).

10416 divided by its sum of digits (12) gives a palindrome (868).

Adding to 10416 its product of nonzero digits (24), we get a triangular number (10440 = T₁₄₄).

10416 divided by its product of nonzero digits (24) gives a palindrome (434).

Adding to 10416 its reverse (61401), we get a palindrome (71817).

It can be divided in two parts, 104 and 16, that added together give a triangular number (120 = T₁₅).

The spelling of 10416 in words is "ten thousand, four hundred sixteen".