414260000 has 240 divisors, whose sum is σ = 1275341760. Its totient is φ = 128640000.

The previous prime is 414259997. The next prime is 414260003. The reversal of 414260000 is 62414.

It is an interprime number because it is at equal distance from previous prime (414259997) and next prime (414260003).

It is a super-2 number, since 2×414260000² = 343222695200000000, which contains 22 as substring.

It is not an unprimeable number, because it can be changed into a prime (414260003) 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, 1539866 + ... + 1540134.

It is an arithmetic number, because the mean of its divisors is an integer number (5313924).

Almost surely, 2^414260000 is an apocalyptic number.

414260000 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 414260000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (637670880).

414260000 is an abundant number, since it is smaller than the sum of its proper divisors (861081760).

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

414260000 is a wasteful number, since it uses less digits than its factorization.

414260000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 317 (or 294 counting only the distinct ones).

The product of its (nonzero) digits is 192, while the sum is 17.

The square root of 414260000 is about 20353.3780979964. The cubic root of 414260000 is about 745.4599804914.

The spelling of 414260000 in words is "four hundred fourteen million, two hundred sixty thousand".