409899600 has 270 divisors, whose sum is σ = 1565197998. Its totient is φ = 99264000.

The previous prime is 409899587. The next prime is 409899613. The reversal of 409899600 is 6998904.

It is an interprime number because it is at equal distance from previous prime (409899587) and next prime (409899613).

It can be written as a sum of positive squares in 3 ways, for example, as 38489616 + 371409984 = 6204^2 + 19272^2 .

It is a Harshad number since it is a multiple of its sum of digits (45).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 53 ways as a sum of consecutive naturals, for example, 435130 + ... + 436070.

Almost surely, 2^409899600 is an apocalyptic number.

409899600 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 409899600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (782598999).

409899600 is an abundant number, since it is smaller than the sum of its proper divisors (1155298398).

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

409899600 is a wasteful number, since it uses less digits than its factorization.

409899600 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 987 (or 962 counting only the distinct ones).

The product of its (nonzero) digits is 139968, while the sum is 45.

The square root of 409899600 is about 20245.9773782349. The cubic root of 409899600 is about 742.8352395627.

It can be divided in two parts, 409 and 899600, that added together give a palindrome (900009).

The spelling of 409899600 in words is "four hundred nine million, eight hundred ninety-nine thousand, six hundred".