101993200 has 120 divisors (see below), whose sum is σ = 265282128. Its totient is φ = 37539840.

The previous prime is 101993189. The next prime is 101993207. The reversal of 101993200 is 2399101.

101993200 = T₁ + T₂ + ... + T₈₄₈.

101993200 is a nontrivial binomial coefficient, being equal to C(850, 3).

It is a super-2 number, since 2×101993200² = 20805225692480000, which contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (25).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (101993207) by changing a digit.

It is the 848-th tetrahedral number.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 360259 + ... + 360541.

Almost surely, 2^101993200 is an apocalyptic number.

101993200 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 101993200, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (132641064).

101993200 is an abundant number, since it is smaller than the sum of its proper divisors (163288928).

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

101993200 is a wasteful number, since it uses less digits than its factorization.

101993200 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 371 (or 360 counting only the distinct ones).

The product of its (nonzero) digits is 486, while the sum is 25.

The square root of 101993200 is about 10099.1682825864. The cubic root of 101993200 is about 467.2224896521. Note that the first 3 decimals are identical.

The spelling of 101993200 in words is "one hundred one million, nine hundred ninety-three thousand, two hundred".