414720000 has 350 divisors, whose sum is σ = 1548209883. Its totient is φ = 110592000.

The previous prime is 414719999. The next prime is 414720001. The reversal of 414720000 is 27414.

It is a happy number.

It is a powerful number, because all its prime factors have an exponent greater than 1 and also an Achilles number because it is not a perfect power.

It is a Jordan-Polya number, since it can be written as (5!)⁴ ⋅ 2!.

It is an interprime number because it is at equal distance from previous prime (414719999) and next prime (414720001).

It can be written as a sum of positive squares in 3 ways, for example, as 95883264 + 318836736 = 9792^2 + 17856^2 .

It is an ABA number since it can be written as A⋅B^A, here for A=2, B=14400.

It is a Harshad number since it is a multiple of its sum of digits (18).

It is not an unprimeable number, because it can be changed into a prime (414720001) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 24 ways as a sum of consecutive naturals, for example, 82943998 + ... + 82944002.

Almost surely, 2^414720000 is an apocalyptic number.

414720000 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 414720000

414720000 is an abundant number, since it is smaller than the sum of its proper divisors (1133489883).

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

414720000 is an frugal number, since it uses more digits than its factorization.

414720000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 58 (or 10 counting only the distinct ones).

The product of its (nonzero) digits is 224, while the sum is 18.

The square root of 414720000 is about 20364.6752981726. The cubic root of 414720000 is about 745.7358014289.

Multiplying 414720000 by its sum of digits (18), we get a square (7464960000 = 86400²).

414720000 divided by its sum of digits (18) gives a square (23040000 = 4800²).

Adding to 414720000 its reverse (27414), we get a palindrome (414747414).

The spelling of 414720000 in words is "four hundred fourteen million, seven hundred twenty thousand".