414382080 has 384 divisors, whose sum is σ = 1585059840. Its totient is φ = 90439680.

The previous prime is 414382079. The next prime is 414382103. The reversal of 414382080 is 80283414.

It is a tau number, because it is divible by the number of its divisors (384).

It is a Harshad number since it is a multiple of its sum of digits (30).

It is a congruent number.

It is an unprimeable number.

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 31 ways as a sum of consecutive naturals, for example, 8816617 + ... + 8816663.

It is an arithmetic number, because the mean of its divisors is an integer number (4127760).

Almost surely, 2^414382080 is an apocalyptic number.

414382080 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 414382080, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (792529920).

414382080 is an abundant number, since it is smaller than the sum of its proper divisors (1170677760).

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

414382080 is a wasteful number, since it uses less digits than its factorization.

414382080 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 125 (or 105 counting only the distinct ones).

The product of its (nonzero) digits is 6144, while the sum is 30.

The square root of 414382080 is about 20356.3768878452. The cubic root of 414382080 is about 745.5332008653.

The spelling of 414382080 in words is "four hundred fourteen million, three hundred eighty-two thousand, eighty".