415242172800 has 2304 divisors, whose sum is σ = 1988872704000. Its totient is φ = 80024371200.

The previous prime is 415242172783. The next prime is 415242172801. The reversal of 415242172800 is 8271242514.

415242172800 is a `hidden beast` number, since 4 + 152 + 421 + 7 + 2 + 80 + 0 = 666.

It is a Harshad number since it is a multiple of its sum of digits (36).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (415242172801) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (17) of ones.

It is a polite number, since it can be written in 287 ways as a sum of consecutive naturals, for example, 1543651066 + ... + 1543651334.

It is an arithmetic number, because the mean of its divisors is an integer number (863226000).

Almost surely, 2^415242172800 is an apocalyptic number.

415242172800 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 415242172800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (994436352000).

415242172800 is an abundant number, since it is smaller than the sum of its proper divisors (1573630531200).

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

415242172800 is a wasteful number, since it uses less digits than its factorization.

415242172800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 369 (or 349 counting only the distinct ones).

The product of its (nonzero) digits is 35840, while the sum is 36.

The spelling of 415242172800 in words is "four hundred fifteen billion, two hundred forty-two million, one hundred seventy-two thousand, eight hundred".