106509312 has 264 divisors, whose sum is σ = 381495296. Its totient is φ = 27869184.

The previous prime is 106509311. The next prime is 106509317. The reversal of 106509312 is 213905601.

106509312 is a `hidden beast` number, since 1 + 0 + 650 + 9 + 3 + 1 + 2 = 666.

It is a super-2 number, since 2×106509312² = 22688467085426688, which contains 22 as substring.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (106509311) 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, 838593 + ... + 838719.

Almost surely, 2^106509312 is an apocalyptic number.

106509312 is a gapful number since it is divisible by the number (12) 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 106509312, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (190747648).

106509312 is an abundant number, since it is smaller than the sum of its proper divisors (274985984).

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

106509312 is a wasteful number, since it uses less digits than its factorization.

106509312 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 173 (or 152 counting only the distinct ones).

The product of its (nonzero) digits is 1620, while the sum is 27.

The square root of 106509312 is about 10320.3348782876. The cubic root of 106509312 is about 474.0191200961.

The spelling of 106509312 in words is "one hundred six million, five hundred nine thousand, three hundred twelve".