10005210072 has 576 divisors, whose sum is σ = 34917442560. Its totient is φ = 2645395200.

The previous prime is 10005210053. The next prime is 10005210139. The reversal of 10005210072 is 27001250001.

10005210072 is digitally balanced in base 2, because in such base it contains all the possibile digits an equal number of times.

It is a Harshad number since it is a multiple of its sum of digits (18).

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (17) of ones.

It is a polite number, since it can be written in 143 ways as a sum of consecutive naturals, for example, 232679283 + ... + 232679325.

It is an arithmetic number, because the mean of its divisors is an integer number (60620560).

Almost surely, 2^10005210072 is an apocalyptic number.

10005210072 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 10005210072, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (17458721280).

10005210072 is an abundant number, since it is smaller than the sum of its proper divisors (24912232488).

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

10005210072 is a wasteful number, since it uses less digits than its factorization.

10005210072 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 128 (or 103 counting only the distinct ones).

The product of its (nonzero) digits is 140, while the sum is 18.

Adding to 10005210072 its reverse (27001250001), we get a palindrome (37006460073).

The spelling of 10005210072 in words is "ten billion, five million, two hundred ten thousand, seventy-two".