137268000 has 384 divisors, whose sum is σ = 528353280. Its totient is φ = 34560000.

The previous prime is 137267987. The next prime is 137268007. The reversal of 137268000 is 862731.

It is a Harshad number since it is a multiple of its sum of digits (27).

It is not an unprimeable number, because it can be changed into a prime (137268007) by changing a digit.

It is a polite number, since it can be written in 63 ways as a sum of consecutive naturals, for example, 3347980 + ... + 3348020.

It is an arithmetic number, because the mean of its divisors is an integer number (1375920).

Almost surely, 2^137268000 is an apocalyptic number.

137268000 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 137268000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (264176640).

137268000 is an abundant number, since it is smaller than the sum of its proper divisors (391085280).

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

137268000 is a wasteful number, since it uses less digits than its factorization.

137268000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 106 (or 82 counting only the distinct ones).

The product of its (nonzero) digits is 2016, while the sum is 27.

The square root of 137268000 is about 11716.1427099536. The cubic root of 137268000 is about 515.8496046281.

The spelling of 137268000 in words is "one hundred thirty-seven million, two hundred sixty-eight thousand".