10006752000 has 288 divisors, whose sum is σ = 37988181504. Its totient is φ = 2287104000.

The previous prime is 10006751971. The next prime is 10006752001. The reversal of 10006752000 is 25760001.

It is a Harshad number since it is a multiple of its sum of digits (21).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (10006752001) by changing a digit.

It is a polite number, since it can be written in 31 ways as a sum of consecutive naturals, for example, 664555 + ... + 679445.

It is an arithmetic number, because the mean of its divisors is an integer number (131903408).

Almost surely, 2^10006752000 is an apocalyptic number.

10006752000 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 10006752000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (18994090752).

10006752000 is an abundant number, since it is smaller than the sum of its proper divisors (27981429504).

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

10006752000 is an equidigital number, since it uses as much as digits as its factorization.

10006752000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 14932 (or 14908 counting only the distinct ones).

The product of its (nonzero) digits is 420, while the sum is 21.

The spelling of 10006752000 in words is "ten billion, six million, seven hundred fifty-two thousand".