3967142400 has 480 divisors, whose sum is σ = 15699203520. Its totient is φ = 975421440.

The previous prime is 3967142369. The next prime is 3967142401. The reversal of 3967142400 is 42417693.

It is a tau number, because it is divible by the number of its divisors (480).

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 (3967142401) by changing a digit.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 4492359 + ... + 4493241.

It is an arithmetic number, because the mean of its divisors is an integer number (32706674).

Almost surely, 2^3967142400 is an apocalyptic number.

3967142400 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 3967142400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (7849601760).

3967142400 is an abundant number, since it is smaller than the sum of its proper divisors (11732061120).

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

3967142400 is a wasteful number, since it uses less digits than its factorization.

3967142400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 933 (or 906 counting only the distinct ones).

The product of its (nonzero) digits is 36288, while the sum is 36.

The square root of 3967142400 is about 62985.2554174388. The cubic root of 3967142400 is about 1583.0425802832.

The spelling of 3967142400 in words is "three billion, nine hundred sixty-seven million, one hundred forty-two thousand, four hundred".