29970 has 40 divisors (see below), whose sum is σ = 82764. Its totient is φ = 7776.

The previous prime is 29959. The next prime is 29983. The reversal of 29970 is 7992.

29970 is nontrivially palindromic in base 14.

It can be written as a sum of positive squares in 2 ways, for example, as 29241 + 729 = 171^2 + 27^2 .

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

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 19 ways as a sum of consecutive naturals, for example, 792 + ... + 828.

2²⁹⁹⁷⁰ is an apocalyptic number.

It is a practical number, because each smaller number is the sum of distinct divisors of 29970, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (41382).

29970 is an abundant number, since it is smaller than the sum of its proper divisors (52794).

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

29970 is a wasteful number, since it uses less digits than its factorization.

29970 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 56 (or 47 counting only the distinct ones).

The product of its (nonzero) digits is 1134, while the sum is 27.

The square root of 29970 is about 173.1184565550. The cubic root of 29970 is about 31.0619641635.

It can be divided in two parts, 29 and 970, that added together give a palindrome (999).

The spelling of 29970 in words is "twenty-nine thousand, nine hundred seventy".