609408000 has 396 divisors, whose sum is σ = 2295677748. Its totient is φ = 155443200.

The previous prime is 609407987. The next prime is 609408017. The reversal of 609408000 is 804906.

It is a powerful number, because all its prime factors have an exponent greater than 1 and also an Achilles number because it is not a perfect power.

It can be written as a sum of positive squares in 2 ways, for example, as 19501056 + 589906944 = 4416^2 + 24288^2 .

It is a super-2 number, since 2×609408000² = 742756220928000000, which contains 22 as substring.

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 35 ways as a sum of consecutive naturals, for example, 26495989 + ... + 26496011.

Almost surely, 2^609408000 is an apocalyptic number.

609408000 is a gapful number since it is divisible by the number (60) 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 609408000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1147838874).

609408000 is an abundant number, since it is smaller than the sum of its proper divisors (1686269748).

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

609408000 is a wasteful number, since it uses less digits than its factorization.

609408000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 87 (or 33 counting only the distinct ones).

The product of its (nonzero) digits is 1728, while the sum is 27.

The square root of 609408000 is about 24686.1904715977. The cubic root of 609408000 is about 847.8181644059.

The spelling of 609408000 in words is "six hundred nine million, four hundred eight thousand".