415254400 has 192 divisors, whose sum is σ = 1147426560. Its totient is φ = 147200000.

The previous prime is 415254383. The next prime is 415254407. The reversal of 415254400 is 4452514.

It is a happy number.

It is a Harshad number since it is a multiple of its sum of digits (25).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (415254407) by changing a digit.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 1654275 + ... + 1654525.

It is an arithmetic number, because the mean of its divisors is an integer number (5976180).

Almost surely, 2^415254400 is an apocalyptic number.

415254400 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 415254400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (573713280).

415254400 is an abundant number, since it is smaller than the sum of its proper divisors (732172160).

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

415254400 is a wasteful number, since it uses less digits than its factorization.

415254400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 333 (or 316 counting only the distinct ones).

The product of its (nonzero) digits is 3200, while the sum is 25.

The square root of 415254400 is about 20377.7918332679. The cubic root of 415254400 is about 746.0559774185.

The spelling of 415254400 in words is "four hundred fifteen million, two hundred fifty-four thousand, four hundred".