414315000 has 480 divisors, whose sum is σ = 1637475840. Its totient is φ = 97200000.

The previous prime is 414314983. The next prime is 414315037. The reversal of 414315000 is 513414.

It is a happy number.

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

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 119 ways as a sum of consecutive naturals, for example, 13364985 + ... + 13365015.

It is an arithmetic number, because the mean of its divisors is an integer number (3411408).

Almost surely, 2^414315000 is an apocalyptic number.

414315000 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 414315000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (818737920).

414315000 is an abundant number, since it is smaller than the sum of its proper divisors (1223160840).

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

414315000 is a wasteful number, since it uses less digits than its factorization.

414315000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 83 (or 52 counting only the distinct ones).

The product of its (nonzero) digits is 240, while the sum is 18.

The square root of 414315000 is about 20354.7291802176. The cubic root of 414315000 is about 745.4929698255.

Adding to 414315000 its reverse (513414), we get a palindrome (414828414).

The spelling of 414315000 in words is "four hundred fourteen million, three hundred fifteen thousand".