45968400 has 135 divisors (see below), whose sum is σ = 160947319. Its totient is φ = 12149760.

The previous prime is 45968383. The next prime is 45968401. The reversal of 45968400 is 486954.

The square root of 45968400 is 6780.

It is a perfect power (a square), and thus also a powerful number.

It can be written as a sum of positive squares in 4 ways, for example, as 23386896 + 22581504 = 4836^2 + 4752^2 .

It is a super-2 number, since 2×45968400² = 4226187597120000, which contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (36).

It is a Duffinian number.

It is not an unprimeable number, because it can be changed into a prime (45968401) by changing a digit.

It is a polite number, since it can be written in 26 ways as a sum of consecutive naturals, for example, 406744 + ... + 406856.

Almost surely, 2^45968400 is an apocalyptic number.

45968400 is a gapful number since it is divisible by the number (40) formed by its first and last digit.

45968400 is the 6780-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 45968400

45968400 is an abundant number, since it is smaller than the sum of its proper divisors (114978919).

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

45968400 is a wasteful number, since it uses less digits than its factorization.

45968400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 250 (or 123 counting only the distinct ones).

The product of its (nonzero) digits is 34560, while the sum is 36.

The cubic root of 45968400 is about 358.2227217035. Note that the first 3 decimals are identical.

Multiplying 45968400 by its sum of digits (36), we get a square (1654862400 = 40680²).

45968400 divided by its sum of digits (36) gives a square (1276900 = 1130²).

It can be divided in two parts, 4596 and 8400, that added together give a square (12996 = 114²).

The spelling of 45968400 in words is "forty-five million, nine hundred sixty-eight thousand, four hundred".