420129600 has 336 divisors, whose sum is σ = 1538264640. Its totient is φ = 99532800.

The previous prime is 420129533. The next prime is 420129607. The reversal of 420129600 is 6921024.

It is a Harshad number since it is a multiple of its sum of digits (24).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (420129607) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 3854346 + ... + 3854454.

Almost surely, 2^420129600 is an apocalyptic number.

420129600 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 420129600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (769132320).

420129600 is an abundant number, since it is smaller than the sum of its proper divisors (1118135040).

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

420129600 is a wasteful number, since it uses less digits than its factorization.

420129600 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 218 (or 203 counting only the distinct ones).

The product of its (nonzero) digits is 864, while the sum is 24.

The square root of 420129600 is about 20497.0632042739. The cubic root of 420129600 is about 748.9642592020.

The spelling of 420129600 in words is "four hundred twenty million, one hundred twenty-nine thousand, six hundred".