414042048 has 168 divisors, whose sum is σ = 1403482080. Its totient is φ = 114186240.

The previous prime is 414042047. The next prime is 414042049. The reversal of 414042048 is 840240414.

It is a happy number.

It is an interprime number because it is at equal distance from previous prime (414042047) and next prime (414042049).

It is a tau number, because it is divible by the number of its divisors (168).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (414042047) by changing a digit.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 115158 + ... + 118698.

It is an arithmetic number, because the mean of its divisors is an integer number (8354060).

Almost surely, 2^414042048 is an apocalyptic number.

414042048 is a gapful number since it is divisible by the number (48) 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 414042048, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (701741040).

414042048 is an abundant number, since it is smaller than the sum of its proper divisors (989440032).

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

414042048 is a wasteful number, since it uses less digits than its factorization.

414042048 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 3595 (or 3582 counting only the distinct ones).

The product of its (nonzero) digits is 4096, while the sum is 27.

The square root of 414042048 is about 20348.0231963697. The cubic root of 414042048 is about 745.3292228385.

The spelling of 414042048 in words is "four hundred fourteen million, forty-two thousand, forty-eight".