45760 has 56 divisors (see below), whose sum is σ = 128016. Its totient is φ = 15360.

The previous prime is 45757. The next prime is 45763. The reversal of 45760 is 6754.

45760 = T₁ + T₂ + ... + T₆₄.

45760 = 20² + 21² + ... + 52².

45760 is a nontrivial binomial coefficient, being equal to C(66, 3).

It is an interprime number because it is at equal distance from previous prime (45757) and next prime (45763).

It is a Harshad number since it is a multiple of its sum of digits (22).

It is not an unprimeable number, because it can be changed into a prime (45763) by changing a digit.

It is the 64-th tetrahedral number.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 3514 + ... + 3526.

It is an arithmetic number, because the mean of its divisors is an integer number (2286).

45760 is a Friedman number, since it can be written as 704*65, using all its digits and the basic arithmetic operations.

2⁴⁵⁷⁶⁰ is an apocalyptic number.

45760 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 45760, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (64008).

45760 is an abundant number, since it is smaller than the sum of its proper divisors (82256).

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

45760 is a wasteful number, since it uses less digits than its factorization.

45760 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 41 (or 31 counting only the distinct ones).

The product of its (nonzero) digits is 840, while the sum is 22.

The square root of 45760 is about 213.9158713139. The cubic root of 45760 is about 35.7680561470.

45760 divided by its sum of digits (22) gives a triangular number (2080 = T₆₄).

The spelling of 45760 in words is "forty-five thousand, seven hundred sixty".