• 30 can be written using four 4's:

See also 113.

• 6² can be partitioned into smaller squares in 42 ways. 30 of these partitions can be actually turned into tilings of a 6×6 square, as depicted below, while others can't, as {1², 1², 3², 3², 4²}.

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30 has 8 divisors (see below), whose sum is σ = 72. Its totient is φ = 8.

The previous prime is 29. The next prime is 31. The reversal of 30 is 3.

30 = 1² + 2² + ... + 4².

It is a primorial, being the product of the first 3 primes.

30 is nontrivially palindromic in base 9 and base 14.

30 is an esthetic number in base 3, because in such base its adjacent digits differ by 1.

It is an interprime number because it is at equal distance from previous prime (29) and next prime (31).

It is a sphenic number, since it is the product of 3 distinct primes.

30 is an admirable number.

It is a Harshad number since it is a multiple of its sum of digits (3).

It is a super Niven number, because it is divisible the sum of any subset of its (nonzero) digits.

30 is an idoneal number.

It is an alternating number because its digits alternate between odd and even.

30 is an undulating number in base 3.

It is a Curzon number.

It is a partition number, being equal to the number of ways a set of 9 identical objects can be partitioned into subset.

30 is a nontrivial repdigit in base 9 and base 14.

It is a plaindrome in base 8, base 9, base 11, base 12, base 13, base 14 and base 16.

It is a nialpdrome in base 2, base 5, base 6, base 7, base 9, base 10, base 14 and base 15.

It is a zygodrome in base 9 and base 14.

It is a congruent number.

A polygon with 30 sides can be constructed with ruler and compass.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 4 + ... + 8.

It is an arithmetic number, because the mean of its divisors is an integer number (9).

30 is a Giuga number.

It is a pronic number, being equal to 5×6.

It is a practical number, because each smaller number is the sum of distinct divisors of 30, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (36).

30 is a primitive abundant number, since it is smaller than the sum of its proper divisors, none of which is abundant.

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

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

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

The sum of its prime factors is 10.

The product of its (nonzero) digits is 3, while the sum is 3.

The square root of 30 is about 5.4772255751. The cubic root of 30 is about 3.1072325060.

The spelling of 30 in words is "thirty", and thus it is an aban number, an eban number, an oban number, and an uban number.