414402120 has 192 divisors, whose sum is σ = 1478917440. Its totient is φ = 99801600.

The previous prime is 414402077. The next prime is 414402127. The reversal of 414402120 is 21204414.

414402120 is a `hidden beast` number, since 414 + 40 + 212 + 0 = 666.

It is a Harshad number since it is a multiple of its sum of digits (18).

It is a junction number, because it is equal to n+sod(n) for n = 414402093 and 414402102.

It is not an unprimeable number, because it can be changed into a prime (414402127) 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, 898690 + ... + 899150.

It is an arithmetic number, because the mean of its divisors is an integer number (7702695).

Almost surely, 2^414402120 is an apocalyptic number.

414402120 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 414402120, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (739458720).

414402120 is an abundant number, since it is smaller than the sum of its proper divisors (1064515320).

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

414402120 is a wasteful number, since it uses less digits than its factorization.

414402120 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 716 (or 709 counting only the distinct ones).

The product of its (nonzero) digits is 256, while the sum is 18.

The square root of 414402120 is about 20356.8691109414. The cubic root of 414402120 is about 745.5452189562.

Adding to 414402120 its reverse (21204414), we get a palindrome (435606534).

The spelling of 414402120 in words is "four hundred fourteen million, four hundred two thousand, one hundred twenty".