105388416 has 144 divisors (see below), whose sum is σ = 352967940. Its totient is φ = 30094848.

The previous prime is 105388403. The next prime is 105388417. The reversal of 105388416 is 614883501.

It is a tau number, because it is divible by the number of its divisors (144).

It is a super-2 number, since 2×105388416² = 22213436453978112, which contains 22 as substring.

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

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (105388417) by changing a digit.

It is a polite number, since it can be written in 17 ways as a sum of consecutive naturals, for example, 55515 + ... + 57381.

Almost surely, 2^105388416 is an apocalyptic number.

105388416 is a gapful number since it is divisible by the number (16) 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 105388416, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (176483970).

105388416 is an abundant number, since it is smaller than the sum of its proper divisors (247579524).

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

105388416 is a wasteful number, since it uses less digits than its factorization.

105388416 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 1901 (or 1879 counting only the distinct ones).

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

The square root of 105388416 is about 10265.8860309279. The cubic root of 105388416 is about 472.3504053178.

It can be divided in two parts, 105 and 388416, that added together give a triangular number (388521 = T₈₈₁).

The spelling of 105388416 in words is "one hundred five million, three hundred eighty-eight thousand, four hundred sixteen".