414742400 has 48 divisors (see below), whose sum is σ = 1024551240. Its totient is φ = 165895680.

The previous prime is 414742351. The next prime is 414742409. The reversal of 414742400 is 4247414.

It is a super-2 number, since 2×414742400² = 344022516715520000, which contains 22 as substring.

It is a self number, because there is not a number n which added to its sum of digits gives 414742400.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (414742409) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 5 ways as a sum of consecutive naturals, for example, 61604 + ... + 68003.

Almost surely, 2^414742400 is an apocalyptic number.

414742400 is a gapful number since it is divisible by the number (40) formed by its first and last digit.

It is an amenable number.

414742400 is an abundant number, since it is smaller than the sum of its proper divisors (609808840).

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

414742400 is a wasteful number, since it uses less digits than its factorization.

414742400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 129631 (or 129614 counting only the distinct ones).

The product of its (nonzero) digits is 3584, while the sum is 26.

The square root of 414742400 is about 20365.2252626874. The cubic root of 414742400 is about 745.7492275005.

Adding to 414742400 its reverse (4247414), we get a palindrome (418989814).

The spelling of 414742400 in words is "four hundred fourteen million, seven hundred forty-two thousand, four hundred".