100506400 has 72 divisors (see below), whose sum is σ = 248866884. Its totient is φ = 39628800.

The previous prime is 100506383. The next prime is 100506401. The reversal of 100506400 is 4605001.

It can be written as a sum of positive squares in 6 ways, for example, as 51897616 + 48608784 = 7204^2 + 6972^2 .

It is a Harshad number since it is a multiple of its sum of digits (16).

It is not an unprimeable number, because it can be changed into a prime (100506401) by changing a digit.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 57540 + ... + 59260.

Almost surely, 2^100506400 is an apocalyptic number.

100506400 is a gapful number since it is divisible by the number (10) 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 100506400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (124433442).

100506400 is an abundant number, since it is smaller than the sum of its proper divisors (148360484).

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

100506400 is a wasteful number, since it uses less digits than its factorization.

100506400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1814 (or 1801 counting only the distinct ones).

The product of its (nonzero) digits is 120, while the sum is 16.

The square root of 100506400 is about 10025.2880257876. The cubic root of 100506400 is about 464.9410647163.

The spelling of 100506400 in words is "one hundred million, five hundred six thousand, four hundred".