157968000 has 192 divisors, whose sum is σ = 567819720. Its totient is φ = 42086400.

The previous prime is 157967951. The next prime is 157968001. The reversal of 157968000 is 869751.

157968000 is a `hidden beast` number, since 1 + 579 + 6 + 80 + 0 + 0 = 666.

It can be written as a sum of positive squares in 4 ways, for example, as 31270464 + 126697536 = 5592^2 + 11256^2 .

It is a tau number, because it is divible by the number of its divisors (192).

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 (157968001) by changing a digit.

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 23 ways as a sum of consecutive naturals, for example, 143452 + ... + 144548.

Almost surely, 2^157968000 is an apocalyptic number.

157968000 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 157968000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (283909860).

157968000 is an abundant number, since it is smaller than the sum of its proper divisors (409851720).

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

157968000 is a wasteful number, since it uses less digits than its factorization.

157968000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1132 (or 1107 counting only the distinct ones).

The product of its (nonzero) digits is 15120, while the sum is 36.

The square root of 157968000 is about 12568.5321338651. The cubic root of 157968000 is about 540.5755180970.

The spelling of 157968000 in words is "one hundred fifty-seven million, nine hundred sixty-eight thousand".