420459600 has 240 divisors, whose sum is σ = 1499529024. Its totient is φ = 99840000.

The previous prime is 420459593. The next prime is 420459617. The reversal of 420459600 is 6954024.

It is a tau number, because it is divible by the number of its divisors (240).

It is a Harshad number since it is a multiple of its sum of digits (30).

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, 699300 + ... + 699900.

Almost surely, 2^420459600 is an apocalyptic number.

420459600 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 420459600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (749764512).

420459600 is an abundant number, since it is smaller than the sum of its proper divisors (1079069424).

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

420459600 is a wasteful number, since it uses less digits than its factorization.

420459600 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 686 (or 675 counting only the distinct ones).

The product of its (nonzero) digits is 8640, while the sum is 30.

The square root of 420459600 is about 20505.1115578531. Note that the first 3 decimals coincide. The cubic root of 420459600 is about 749.1603046776.

The spelling of 420459600 in words is "four hundred twenty million, four hundred fifty-nine thousand, six hundred".