420416172000 has 1152 divisors, whose sum is σ = 1754434805760. Its totient is φ = 94279680000.

The previous prime is 420416171951. The next prime is 420416172019. The reversal of 420416172000 is 271614024.

420416172000 is a `hidden beast` number, since 4 + 2 + 0 + 41 + 617 + 2 + 0 + 0 + 0 = 666.

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (19) of ones.

It is a polite number, since it can be written in 191 ways as a sum of consecutive naturals, for example, 282347256 + ... + 282348744.

It is an arithmetic number, because the mean of its divisors is an integer number (1522946880).

Almost surely, 2^420416172000 is an apocalyptic number.

420416172000 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 420416172000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (877217402880).

420416172000 is an abundant number, since it is smaller than the sum of its proper divisors (1334018633760).

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

420416172000 is a wasteful number, since it uses less digits than its factorization.

420416172000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1585 (or 1564 counting only the distinct ones).

The product of its (nonzero) digits is 2688, while the sum is 27.

Adding to 420416172000 its reverse (271614024), we get a palindrome (420687786024).

It can be divided in two parts, 420416 and 172000, that added together give a triangular number (592416 = T₁₀₈₈).

The spelling of 420416172000 in words is "four hundred twenty billion, four hundred sixteen million, one hundred seventy-two thousand".