3967178342400 has 2688 divisors, whose sum is σ = 18403689692640. Its totient is φ = 825564856320.

The previous prime is 3967178342381. The next prime is 3967178342429. The reversal of 3967178342400 is 42438717693.

3967178342400 is a `hidden beast` number, since 3 + 9 + 67 + 178 + 3 + 4 + 2 + 400 = 666.

It is a tau number, because it is divible by the number of its divisors (2688).

It is a super-2 number, since 2×3967178342400² (a number of 26 digits) contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (54).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 167 ways as a sum of consecutive naturals, for example, 54344908764 + ... + 54344908836.

Almost surely, 2^{3967178342400} is an apocalyptic number.

3967178342400 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 3967178342400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (9201844846320).

3967178342400 is an abundant number, since it is smaller than the sum of its proper divisors (14436511350240).

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

3967178342400 is an frugal number, since it uses more digits than its factorization.

3967178342400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 151 (or 103 counting only the distinct ones).

The product of its (nonzero) digits is 6096384, while the sum is 54.

The spelling of 3967178342400 in words is "three trillion, nine hundred sixty-seven billion, one hundred seventy-eight million, three hundred forty-two thousand, four hundred".