416229840 has 360 divisors, whose sum is σ = 1588809768. Its totient is φ = 100776960.

The previous prime is 416229833. The next prime is 416229851. The reversal of 416229840 is 48922614.

It can be written as a sum of positive squares in 4 ways, for example, as 12702096 + 403527744 = 3564^2 + 20088^2 .

It is a tau number, because it is divible by the number of its divisors (360).

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 = 416229795 and 416229804.

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 71 ways as a sum of consecutive naturals, for example, 6823410 + ... + 6823470.

Almost surely, 2^416229840 is an apocalyptic number.

416229840 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 416229840, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (794404884).

416229840 is an abundant number, since it is smaller than the sum of its proper divisors (1172579928).

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

416229840 is an equidigital number, since it uses as much as digits as its factorization.

416229840 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 111 (or 84 counting only the distinct ones).

The product of its (nonzero) digits is 27648, while the sum is 36.

The square root of 416229840 is about 20401.7116928948. The cubic root of 416229840 is about 746.6396868794.

The spelling of 416229840 in words is "four hundred sixteen million, two hundred twenty-nine thousand, eight hundred forty".