419952960 has 336 divisors, whose sum is σ = 1698443136. Its totient is φ = 93229056.

The previous prime is 419952959. The next prime is 419953003. The reversal of 419952960 is 69259914.

It is a tau number, because it is divible by the number of its divisors (336).

It is a super-2 number, since 2×419952960² = 352720977225523200, which contains 22 as substring.

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

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 745639 + ... + 746201.

Almost surely, 2^419952960 is an apocalyptic number.

419952960 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 419952960, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (849221568).

419952960 is an abundant number, since it is smaller than the sum of its proper divisors (1278490176).

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

419952960 is a wasteful number, since it uses less digits than its factorization.

419952960 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 630 (or 617 counting only the distinct ones).

The product of its (nonzero) digits is 174960, while the sum is 45.

The square root of 419952960 is about 20492.7538412972. The cubic root of 419952960 is about 748.8592792211.

The spelling of 419952960 in words is "four hundred nineteen million, nine hundred fifty-two thousand, nine hundred sixty".