420782400 has 126 divisors (see below), whose sum is σ = 1495611182. Its totient is φ = 112204800.

The previous prime is 420782393. The next prime is 420782413. The reversal of 420782400 is 4287024.

It can be written as a sum of positive squares in 3 ways, for example, as 1679616 + 419102784 = 1296^2 + 20472^2 .

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 17 ways as a sum of consecutive naturals, for example, 211 + ... + 29010.

Almost surely, 2^420782400 is an apocalyptic number.

420782400 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 420782400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (747805591).

420782400 is an abundant number, since it is smaller than the sum of its proper divisors (1074828782).

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

420782400 is a wasteful number, since it uses less digits than its factorization.

420782400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 29249 (or 29231 counting only the distinct ones).

The product of its (nonzero) digits is 3584, while the sum is 27.

The square root of 420782400 is about 20512.9812557804. The cubic root of 420782400 is about 749.3519735769.

The spelling of 420782400 in words is "four hundred twenty million, seven hundred eighty-two thousand, four hundred".