416640000 has 440 divisors, whose sum is σ = 1637075968. Its totient is φ = 92160000.

The previous prime is 416639989. The next prime is 416640001. The reversal of 416640000 is 46614.

It is a hoax number, since the sum of its digits (21) coincides with the sum of the digits of its distinct prime factors.

It is a Harshad number since it is a multiple of its sum of digits (21).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (416640001) 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 39 ways as a sum of consecutive naturals, for example, 13439985 + ... + 13440015.

Almost surely, 2^416640000 is an apocalyptic number.

416640000 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 416640000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (818537984).

416640000 is an abundant number, since it is smaller than the sum of its proper divisors (1220435968).

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

416640000 is an equidigital number, since it uses as much as digits as its factorization.

416640000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 81 (or 48 counting only the distinct ones).

The product of its (nonzero) digits is 576, while the sum is 21.

The square root of 416640000 is about 20411.7613154769. The cubic root of 416640000 is about 746.8848568694.

Adding to 416640000 its reverse (46614), we get a palindrome (416686614).

The spelling of 416640000 in words is "four hundred sixteen million, six hundred forty thousand".