137972800 has 168 divisors, whose sum is σ = 395085824. Its totient is φ = 46448640.

The previous prime is 137972797. The next prime is 137972801. The reversal of 137972800 is 8279731.

137972800 is digitally balanced in base 3, because in such base it contains all the possibile digits an equal number of times.

It is a self number, because there is not a number n which added to its sum of digits gives 137972800.

It is not an unprimeable number, because it can be changed into a prime (137972801) by changing a digit.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 1086337 + ... + 1086463.

Almost surely, 2^137972800 is an apocalyptic number.

137972800 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 137972800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (197542912).

137972800 is an abundant number, since it is smaller than the sum of its proper divisors (257113024).

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

137972800 is a wasteful number, since it uses less digits than its factorization.

137972800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 253 (or 238 counting only the distinct ones).

The product of its (nonzero) digits is 21168, while the sum is 37.

The square root of 137972800 is about 11746.1823585368. The cubic root of 137972800 is about 516.7309713002.

The spelling of 137972800 in words is "one hundred thirty-seven million, nine hundred seventy-two thousand, eight hundred".