37721408400 has 675 divisors, whose sum is σ = 148381416579. Its totient is φ = 9173399040.

The previous prime is 37721408371. The next prime is 37721408401. The reversal of 37721408400 is 480412773.

It is a happy number.

The square root of 37721408400 is 194220.

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

37721408400 is a `hidden beast` number, since 37 + 7 + 214 + 0 + 8 + 400 = 666.

It can be written as a sum of positive squares in 4 ways, for example, as 9722748816 + 27998659584 = 98604^2 + 167328^2 .

It is a tau number, because it is divible by the number of its divisors (675).

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

It is not an unprimeable number, because it can be changed into a prime (37721408401) by changing a digit.

It is a polite number, since it can be written in 134 ways as a sum of consecutive naturals, for example, 454474759 + ... + 454474841.

Almost surely, 2^37721408400 is an apocalyptic number.

37721408400 is a gapful number since it is divisible by the number (30) formed by its first and last digit.

37721408400 is the 194220-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 37721408400

37721408400 is an abundant number, since it is smaller than the sum of its proper divisors (110660008179).

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

37721408400 is a wasteful number, since it uses less digits than its factorization.

37721408400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 222 (or 106 counting only the distinct ones).

The product of its (nonzero) digits is 37632, while the sum is 36.

Multiplying 37721408400 by its sum of digits (36), we get a square (1357970702400 = 1165320²).

37721408400 divided by its sum of digits (36) gives a square (1047816900 = 32370²).

The spelling of 37721408400 in words is "thirty-seven billion, seven hundred twenty-one million, four hundred eight thousand, four hundred".