407967840 has 288 divisors, whose sum is σ = 1651104000. Its totient is φ = 93187584.

The previous prime is 407967823. The next prime is 407967841. The reversal of 407967840 is 48769704.

It is a tau number, because it is divible by the number of its divisors (288).

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

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (407967841) by changing a digit.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 271411 + ... + 272909.

It is an arithmetic number, because the mean of its divisors is an integer number (5733000).

Almost surely, 2^407967840 is an apocalyptic number.

407967840 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 407967840, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (825552000).

407967840 is an abundant number, since it is smaller than the sum of its proper divisors (1243136160).

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

407967840 is a wasteful number, since it uses less digits than its factorization.

407967840 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1536 (or 1516 counting only the distinct ones).

The product of its (nonzero) digits is 338688, while the sum is 45.

The square root of 407967840 is about 20198.2137824116. The cubic root of 407967840 is about 741.6664659063. Note that the first 3 decimals are identical.

The spelling of 407967840 in words is "four hundred seven million, nine hundred sixty-seven thousand, eight hundred forty".