1965616800 has 288 divisors, whose sum is σ = 7631511552. Its totient is φ = 429665280.

The previous prime is 1965616787. The next prime is 1965616813. The reversal of 1965616800 is 86165691.

It is a happy number.

It is an interprime number because it is at equal distance from previous prime (1965616787) and next prime (1965616813).

It is a hoax number, since the sum of its digits (42) coincides with the sum of the digits of its distinct prime factors.

It is a Harshad number since it is a multiple of its sum of digits (42).

It is an unprimeable number.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 383857 + ... + 388943.

It is an arithmetic number, because the mean of its divisors is an integer number (26498304).

Almost surely, 2^1965616800 is an apocalyptic number.

1965616800 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 1965616800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (3815755776).

1965616800 is an abundant number, since it is smaller than the sum of its proper divisors (5665894752).

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

1965616800 is a wasteful number, since it uses less digits than its factorization.

1965616800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 5140 (or 5127 counting only the distinct ones).

The product of its (nonzero) digits is 77760, while the sum is 42.

The square root of 1965616800 is about 44335.2771503686. The cubic root of 1965616800 is about 1252.6592560075.

The spelling of 1965616800 in words is "one billion, nine hundred sixty-five million, six hundred sixteen thousand, eight hundred".