• 45 can be written using four 4's:

45 has 6 divisors (see below), whose sum is σ = 78. Its totient is φ = 24.

The previous prime is 43. The next prime is 47. The reversal of 45 is 54.

45 is nontrivially palindromic in base 2, base 8 and base 14.

45 is an esthetic number in base 10, because in such base its adjacent digits differ by 1.

45 is a nontrivial binomial coefficient, being equal to C(10, 2).

It is an interprime number because it is at equal distance from previous prime (43) and next prime (47).

It can be written as a sum of positive squares in only one way, i.e., 36 + 9 = 6^2 + 3^2 .

It is not a de Polignac number, because 45 - 2^{1} = 43 is a prime.

It is a Harshad number since it is a multiple of its sum of digits (9), and also a Moran number because the ratio is a prime number: 5 = 45 / (4 + 5).

45 is an idoneal number.

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

45 is a nontrivial repdigit in base 8 and base 14.

It is a plaindrome in base 6, base 8, base 10, base 12, base 13, base 14 and base 16.

It is a nialpdrome in base 7, base 8, base 9, base 11, base 14 and base 15.

It is a zygodrome in base 8 and base 14.

It is a congruent number.

It is a panconsummate number.

It is a Kaprekar number, because its square (2025) can be partitioned into two parts whose sum is 45.

It is a polite number, since it can be written in 5 ways as a sum of consecutive naturals, for example, 7 + ... + 11.

It is an arithmetic number, because the mean of its divisors is an integer number (13).

45 is the 9-th triangular number and also the 5-th hexagonal number.

It is an amenable number.

45 is a deficient number, since it is larger than the sum of its proper divisors (33).

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

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

The sum of its prime factors is 11 (or 8 counting only the distinct ones).

The product of its digits is 20, while the sum is 9.

The square root of 45 is about 6.7082039325. The cubic root of 45 is about 3.5568933045.

Subtracting from 45 its product of digits (20), we obtain a square (25 = 5^{2}).

Multiplying 45 by its product of digits (20), we get a square (900 = 30^{2}).

Adding to 45 its reverse (54), we get a palindrome (99).

The spelling of 45 in words is "forty-five", and thus it is an aban number and an uban number.

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