414362564100 has 243 divisors, whose sum is σ = 1332373513653. Its totient is φ = 107710706880.

The previous prime is 414362564087. The next prime is 414362564131. The reversal of 414362564100 is 1465263414.

The square root of 414362564100 is 643710.

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

414362564100 is a `hidden beast` number, since 4 + 1 + 4 + 3 + 6 + 2 + 5 + 641 + 0 + 0 = 666.

414362564100 is digitally balanced in base 4, because in such base it contains all the possibile digits an equal number of times.

It can be written as a sum of positive squares in only one way, i.e., 149170523076 + 265192041024 = 386226^2 + 514968^2 .

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

It is an unprimeable number.

It is a polite number, since it can be written in 80 ways as a sum of consecutive naturals, for example, 830385651 + ... + 830386149.

Almost surely, 2^414362564100 is an apocalyptic number.

414362564100 is the 643710-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 414362564100

414362564100 is an abundant number, since it is smaller than the sum of its proper divisors (918010949553).

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

414362564100 is a wasteful number, since it uses less digits than its factorization.

414362564100 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 1104 (or 552 counting only the distinct ones).

The product of its (nonzero) digits is 69120, while the sum is 36.

Multiplying 414362564100 by its sum of digits (36), we get a square (14917052307600 = 3862260²).

414362564100 divided by its sum of digits (36) gives a square (11510071225 = 107285²).

The spelling of 414362564100 in words is "four hundred fourteen billion, three hundred sixty-two million, five hundred sixty-four thousand, one hundred".