414185940 has 384 divisors, whose sum is σ = 1591296000. Its totient is φ = 87340032.

The previous prime is 414185923. The next prime is 414185957. The reversal of 414185940 is 49581414.

It is an interprime number because it is at equal distance from previous prime (414185923) and next prime (414185957).

It is a Harshad number since it is a multiple of its sum of digits (36).

It is a junction number, because it is equal to n+sod(n) for n = 414185895 and 414185904.

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 127 ways as a sum of consecutive naturals, for example, 5242821 + ... + 5242899.

It is an arithmetic number, because the mean of its divisors is an integer number (4144000).

Almost surely, 2^414185940 is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 414185940, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (795648000).

414185940 is an abundant number, since it is smaller than the sum of its proper divisors (1177110060).

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

414185940 is a wasteful number, since it uses less digits than its factorization.

414185940 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 196 (or 188 counting only the distinct ones).

The product of its (nonzero) digits is 23040, while the sum is 36.

The square root of 414185940 is about 20351.5586626676. The cubic root of 414185940 is about 745.4155542402.

The spelling of 414185940 in words is "four hundred fourteen million, one hundred eighty-five thousand, nine hundred forty".