407248128 has 288 divisors, whose sum is σ = 1452057600. Its totient is φ = 109983744.

The previous prime is 407248123. The next prime is 407248129. The reversal of 407248128 is 821842704.

407248128 is a `hidden beast` number, since 407 + 248 + 1 + 2 + 8 = 666.

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 (36).

It is a junction number, because it is equal to n+sod(n) for n = 407248092 and 407248101.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (407248123) by changing a digit.

It is a polite number, since it can be written in 31 ways as a sum of consecutive naturals, for example, 919075 + ... + 919517.

Almost surely, 2^407248128 is an apocalyptic number.

407248128 is a gapful number since it is divisible by the number (48) 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 407248128, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (726028800).

407248128 is an abundant number, since it is smaller than the sum of its proper divisors (1044809472).

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

407248128 is a wasteful number, since it uses less digits than its factorization.

407248128 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 494 (or 474 counting only the distinct ones).

The product of its (nonzero) digits is 28672, while the sum is 36.

The square root of 407248128 is about 20180.3896890025. The cubic root of 407248128 is about 741.2300749279.

The spelling of 407248128 in words is "four hundred seven million, two hundred forty-eight thousand, one hundred twenty-eight".