101925172800 has 2016 divisors, whose sum is σ = 458440657920. Its totient is φ = 21897216000.

The previous prime is 101925172793. The next prime is 101925172807. The reversal of 101925172800 is 8271529101.

It is a happy number.

It is an interprime number because it is at equal distance from previous prime (101925172793) and next prime (101925172807).

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

It is not an unprimeable number, because it can be changed into a prime (101925172807) by changing a digit.

It is a polite number, since it can be written in 287 ways as a sum of consecutive naturals, for example, 2754734382 + ... + 2754734418.

It is an arithmetic number, because the mean of its divisors is an integer number (227401120).

Almost surely, 2^101925172800 is an apocalyptic number.

101925172800 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 101925172800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (229220328960).

101925172800 is an abundant number, since it is smaller than the sum of its proper divisors (356515485120).

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

101925172800 is a wasteful number, since it uses less digits than its factorization.

101925172800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 138 (or 106 counting only the distinct ones).

The product of its (nonzero) digits is 10080, while the sum is 36.

The spelling of 101925172800 in words is "one hundred one billion, nine hundred twenty-five million, one hundred seventy-two thousand, eight hundred".