407072000 has 72 divisors (see below), whose sum is σ = 1014146952. Its totient is φ = 162816000.

The previous prime is 407071999. The next prime is 407072041. The reversal of 407072000 is 270704.

It can be written as a sum of positive squares in 4 ways, for example, as 1024 + 407070976 = 32^2 + 20176^2 .

It is a super-2 number, since 2×407072000² = 331415226368000000, which contains 22 as substring.

It is a hoax number, since the sum of its digits (20) coincides with the sum of the digits of its distinct prime factors.

It is a Harshad number since it is a multiple of its sum of digits (20).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 25640 + ... + 38360.

Almost surely, 2^407072000 is an apocalyptic number.

407072000 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 407072000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (507073476).

407072000 is an abundant number, since it is smaller than the sum of its proper divisors (607074952).

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

407072000 is an equidigital number, since it uses as much as digits as its factorization.

407072000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 12752 (or 12728 counting only the distinct ones).

The product of its (nonzero) digits is 392, while the sum is 20.

The square root of 407072000 is about 20176.0253766692. The cubic root of 407072000 is about 741.1232029854.

The spelling of 407072000 in words is "four hundred seven million, seventy-two thousand".