137314713600 has 405 divisors, whose sum is σ = 494438596743. Its totient is φ = 36427530240.

The previous prime is 137314713521. The next prime is 137314713607. The reversal of 137314713600 is 6317413731.

The square root of 137314713600 is 370560.

It is a perfect power (a square), and thus also a powerful number.

137314713600 is a `hidden beast` number, since 1 + 3 + 7 + 3 + 1 + 47 + 1 + 3 + 600 = 666.

It can be written as a sum of positive squares in 4 ways, for example, as 22084337664 + 115230375936 = 148608^2 + 339456^2 .

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 (137314713607) by changing a digit.

It is a polite number, since it can be written in 26 ways as a sum of consecutive naturals, for example, 711475104 + ... + 711475296.

Almost surely, 2^137314713600 is an apocalyptic number.

137314713600 is a gapful number since it is divisible by the number (10) formed by its first and last digit.

137314713600 is the 370560-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 137314713600

137314713600 is an abundant number, since it is smaller than the sum of its proper divisors (357123883143).

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

137314713600 is an frugal number, since it uses more digits than its factorization.

137314713600 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 430 (or 203 counting only the distinct ones).

The product of its (nonzero) digits is 31752, while the sum is 36.

Multiplying 137314713600 by its sum of digits (36), we get a square (4943329689600 = 2223360²).

137314713600 divided by its sum of digits (36) gives a square (3814297600 = 61760²).

The spelling of 137314713600 in words is "one hundred thirty-seven billion, three hundred fourteen million, seven hundred thirteen thousand, six hundred".