137680000 has 80 divisors (see below), whose sum is σ = 342944910. Its totient is φ = 55040000.

The previous prime is 137679979. The next prime is 137680007. The reversal of 137680000 is 86731.

It can be written as a sum of positive squares in 5 ways, for example, as 7354944 + 130325056 = 2712^2 + 11416^2 .

It is a tau number, because it is divible by the number of its divisors (80).

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

It is not an unprimeable number, because it can be changed into a prime (137680007) by changing a digit.

It is a polite number, since it can be written in 9 ways as a sum of consecutive naturals, for example, 79140 + ... + 80860.

Almost surely, 2^137680000 is an apocalyptic number.

137680000 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 137680000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (171472455).

137680000 is an abundant number, since it is smaller than the sum of its proper divisors (205264910).

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

137680000 is an frugal number, since it uses more digits than its factorization.

137680000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1755 (or 1728 counting only the distinct ones).

The product of its (nonzero) digits is 1008, while the sum is 25.

The square root of 137680000 is about 11733.7121150981. The cubic root of 137680000 is about 516.3651842722.

The spelling of 137680000 in words is "one hundred thirty-seven million, six hundred eighty thousand".