3965950310400 has 1296 divisors, whose sum is σ = 15539822887680. Its totient is φ = 966131712000.

The previous prime is 3965950310389. The next prime is 3965950310419. The reversal of 3965950310400 is 40130595693.

3965950310400 is a `hidden beast` number, since 3 + 9 + 6 + 595 + 0 + 3 + 10 + 40 + 0 = 666.

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 polite number, since it can be written in 107 ways as a sum of consecutive naturals, for example, 9890150200 + ... + 9890150600.

It is an arithmetic number, because the mean of its divisors is an integer number (11990604080).

Almost surely, 2^{3965950310400} is an apocalyptic number.

3965950310400 is a gapful number since it is divisible by the number (30) 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 3965950310400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (7769911443840).

3965950310400 is an abundant number, since it is smaller than the sum of its proper divisors (11573872577280).

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

3965950310400 is a wasteful number, since it uses less digits than its factorization.

3965950310400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 592 (or 551 counting only the distinct ones).

The product of its (nonzero) digits is 437400, while the sum is 45.

It can be divided in two parts, 3965950 and 310400, that added together give a triangular number (4276350 = T₂₉₂₄).

The spelling of 3965950310400 in words is "three trillion, nine hundred sixty-five billion, nine hundred fifty million, three hundred ten thousand, four hundred".