13780 has 24 divisors (see below), whose sum is σ = 31752. Its totient is φ = 4992.

The previous prime is 13763. The next prime is 13781. The reversal of 13780 is 8731.

13780 = T₈₁ + T₈₂ + ... + T₈₄.

13780 = 23² + 24² + ... + 37².

It can be written as a sum of positive squares in 4 ways, for example, as 784 + 12996 = 28^2 + 114^2 .

It is a hoax number, since the sum of its digits (19) coincides with the sum of the digits of its distinct prime factors.

It is an Ulam number.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (13781) by changing a digit.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 234 + ... + 286.

It is an arithmetic number, because the mean of its divisors is an integer number (1323).

2¹³⁷⁸⁰ is an apocalyptic number.

13780 is a gapful number since it is divisible by the number (10) 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 13780, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (15876).

13780 is an abundant number, since it is smaller than the sum of its proper divisors (17972).

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

13780 is a wasteful number, since it uses less digits than its factorization.

13780 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 75 (or 73 counting only the distinct ones).

The product of its (nonzero) digits is 168, while the sum is 19.

The square root of 13780 is about 117.3882447266. The cubic root of 13780 is about 23.9745099741.

The spelling of 13780 in words is "thirteen thousand, seven hundred eighty".