106584138000 has 480 divisors, whose sum is σ = 386309274624. Its totient is φ = 27360000000.

The previous prime is 106584137951. The next prime is 106584138013. The reversal of 106584138000 is 831485601.

It is a super-2 number, since 2×106584138000² (a number of 23 digits) contains 22 as substring.

It is a hoax number, since the sum of its digits (36) coincides with the sum of the digits of its distinct prime factors.

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

It is an unprimeable number.

It is a polite number, since it can be written in 95 ways as a sum of consecutive naturals, for example, 140057620 + ... + 140058380.

Almost surely, 2^106584138000 is an apocalyptic number.

106584138000 is a gapful number since it is divisible by the number (10) 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 106584138000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (193154637312).

106584138000 is an abundant number, since it is smaller than the sum of its proper divisors (279725136624).

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

106584138000 is a wasteful number, since it uses less digits than its factorization.

106584138000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 1072 (or 1053 counting only the distinct ones).

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

The spelling of 106584138000 in words is "one hundred six billion, five hundred eighty-four million, one hundred thirty-eight thousand".