4131972000 has 672 divisors, whose sum is σ = 16542686160. Its totient is φ = 1007769600.

The previous prime is 4131971993. The next prime is 4131972071. The reversal of 4131972000 is 2791314.

It can be written as a sum of positive squares in 8 ways, for example, as 30338064 + 4101633936 = 5508^2 + 64044^2 .

It is a Harshad number since it is a multiple of its sum of digits (27).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 111 ways as a sum of consecutive naturals, for example, 37907946 + ... + 37908054.

Almost surely, 2^4131972000 is an apocalyptic number.

4131972000 is a gapful number since it is divisible by the number (40) 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 4131972000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (8271343080).

4131972000 is an abundant number, since it is smaller than the sum of its proper divisors (12410714160).

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

4131972000 is a wasteful number, since it uses less digits than its factorization.

4131972000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 165 (or 132 counting only the distinct ones).

The product of its (nonzero) digits is 1512, while the sum is 27.

The square root of 4131972000 is about 64280.4169245969. The cubic root of 4131972000 is about 1604.6702091202.

The spelling of 4131972000 in words is "four billion, one hundred thirty-one million, nine hundred seventy-two thousand".