100309968 has 240 divisors, whose sum is σ = 336436800. Its totient is φ = 28512000.

The previous prime is 100309967. The next prime is 100309981. The reversal of 100309968 is 869903001.

It is a super-2 number, since 2×100309968² = 20124179360322048, 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 (100309967) by changing a digit.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 993118 + ... + 993218.

It is an arithmetic number, because the mean of its divisors is an integer number (1401820).

Almost surely, 2^100309968 is an apocalyptic number.

100309968 is a gapful number since it is divisible by the number (18) 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 100309968, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (168218400).

100309968 is an abundant number, since it is smaller than the sum of its proper divisors (236126832).

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

100309968 is a wasteful number, since it uses less digits than its factorization.

100309968 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 159 (or 136 counting only the distinct ones).

The product of its (nonzero) digits is 11664, while the sum is 36.

The square root of 100309968 is about 10015.4864085575. The cubic root of 100309968 is about 464.6379700325.

The spelling of 100309968 in words is "one hundred million, three hundred nine thousand, nine hundred sixty-eight".