47952000 has 320 divisors, whose sum is σ = 182908440. Its totient is φ = 12441600.

The previous prime is 47951999. The next prime is 47952007. The reversal of 47952000 is 25974.

It can be written as a sum of positive squares in 4 ways, for example, as 24681024 + 23270976 = 4968^2 + 4824^2 .

It is a tau number, because it is divible by the number of its divisors (320).

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

It is not an unprimeable number, because it can be changed into a prime (47952007) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 39 ways as a sum of consecutive naturals, for example, 1295982 + ... + 1296018.

Almost surely, 2^47952000 is an apocalyptic number.

47952000 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 47952000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (91454220).

47952000 is an abundant number, since it is smaller than the sum of its proper divisors (134956440).

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

47952000 is an equidigital number, since it uses as much as digits as its factorization.

47952000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 78 (or 47 counting only the distinct ones).

The product of its (nonzero) digits is 2520, while the sum is 27.

The square root of 47952000 is about 6924.7382622017. The cubic root of 47952000 is about 363.3029367907.

Adding to 47952000 its reverse (25974), we get a palindrome (47977974).

The spelling of 47952000 in words is "forty-seven million, nine hundred fifty-two thousand".