46400 has 42 divisors (see below), whose sum is σ = 118110. Its totient is φ = 17920.

The previous prime is 46399. The next prime is 46411. The reversal of 46400 is 464.

46400 = T₄₈ + T₄₉ + ... + T₇₂.

It is a happy number.

It can be written as a sum of positive squares in 3 ways, for example, as 3136 + 43264 = 56^2 + 208^2 .

It is an Ulam number.

It is a nialpdrome in base 16.

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 5 ways as a sum of consecutive naturals, for example, 1586 + ... + 1614.

2⁴⁶⁴⁰⁰ is an apocalyptic number.

46400 is a gapful number since it is divisible by the number (40) 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 46400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (59055).

46400 is an abundant number, since it is smaller than the sum of its proper divisors (71710).

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

46400 is a wasteful number, since it uses less digits than its factorization.

46400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 51 (or 36 counting only the distinct ones).

The product of its (nonzero) digits is 96, while the sum is 14.

The square root of 46400 is about 215.4065922854. The cubic root of 46400 is about 35.9340355829.

Adding to 46400 its reverse (464), we get a palindrome (46864).

Multiplying 46400 by its reverse (464), we get a square (21529600 = 4640²).

46400 divided by its reverse (464) gives a square (100 = 10²).

It can be divided in two parts, 4 and 6400, that multiplied together give a square (25600 = 160²).

The spelling of 46400 in words is "forty-six thousand, four hundred".