106542072000 has 2016 divisors, whose sum is σ = 503136676224. Its totient is φ = 21288960000.

The previous prime is 106542071989. The next prime is 106542072011. The reversal of 106542072000 is 270245601.

106542072000 is a `hidden beast` number, since 1 + 0 + 654 + 2 + 0 + 7 + 2 + 0 + 0 + 0 = 666.

It is an interprime number because it is at equal distance from previous prime (106542071989) and next prime (106542072011).

It is a tau number, because it is divible by the number of its divisors (2016).

It is a super-2 number, since 2×106542072000² (a number of 23 digits) contains 22 as substring.

It is a zygodrome in base 2.

It is an unprimeable number.

It is a polite number, since it can be written in 287 ways as a sum of consecutive naturals, for example, 1054871950 + ... + 1054872050.

It is an arithmetic number, because the mean of its divisors is an integer number (249571764).

Almost surely, 2^106542072000 is an apocalyptic number.

106542072000 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 106542072000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (251568338112).

106542072000 is an abundant number, since it is smaller than the sum of its proper divisors (396594604224).

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

106542072000 is a wasteful number, since it uses less digits than its factorization.

106542072000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 184 (or 154 counting only the distinct ones).

The product of its (nonzero) digits is 3360, while the sum is 27.

The spelling of 106542072000 in words is "one hundred six billion, five hundred forty-two million, seventy-two thousand".