137952460800 has 1536 divisors, whose sum is σ = 639705484800. Its totient is φ = 28665446400.

The previous prime is 137952460747. The next prime is 137952460813. The reversal of 137952460800 is 8064259731.

It is a Jordan-Polya number, since it can be written as 12! ⋅ 4! ⋅ 3! ⋅ 2!.

137952460800 is a `hidden beast` number, since 1 + 37 + 9 + 5 + 2 + 4 + 608 + 0 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (1536).

It is a Harshad number since it is a multiple of its sum of digits (45).

It is a congruent number.

It is an unprimeable 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 95 ways as a sum of consecutive naturals, for example, 12541132795 + ... + 12541132805.

It is an arithmetic number, because the mean of its divisors is an integer number (416474925).

It is a 1-persistent number, because it is pandigital, but 2⋅137952460800 = 275904921600 is not.

Almost surely, 2^137952460800 is an apocalyptic number.

137952460800 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 137952460800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (319852742400).

137952460800 is an abundant number, since it is smaller than the sum of its proper divisors (501753024000).

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

137952460800 is an frugal number, since it uses more digits than its factorization.

137952460800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 79 (or 28 counting only the distinct ones).

The product of its (nonzero) digits is 362880, while the sum is 45.

The spelling of 137952460800 in words is "one hundred thirty-seven billion, nine hundred fifty-two million, four hundred sixty thousand, eight hundred".