414961920 has 144 divisors (see below), whose sum is σ = 1472661120. Its totient is φ = 110647296.

The previous prime is 414961909. The next prime is 414961933. The reversal of 414961920 is 29169414.

It is a happy number.

414961920 is a `hidden beast` number, since 4 + 14 + 9 + 619 + 20 = 666.

It is a tau number, because it is divible by the number of its divisors (144).

It is a Harshad number since it is a multiple of its sum of digits (36).

It is an unprimeable number.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 28557 + ... + 40563.

Almost surely, 2^414961920 is an apocalyptic number.

414961920 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 414961920, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (736330560).

414961920 is an abundant number, since it is smaller than the sum of its proper divisors (1057699200).

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

414961920 is a wasteful number, since it uses less digits than its factorization.

414961920 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 12037 (or 12017 counting only the distinct ones).

The product of its (nonzero) digits is 15552, while the sum is 36.

The square root of 414961920 is about 20370.6141291813. The cubic root of 414961920 is about 745.8807774264.

The spelling of 414961920 in words is "four hundred fourteen million, nine hundred sixty-one thousand, nine hundred twenty".