49680 has 80 divisors (see below), whose sum is σ = 178560. Its totient is φ = 12672.

The previous prime is 49669. The next prime is 49681. The reversal of 49680 is 8694.

49680 = 35² + 36² + ... + 57².

It is a tau number, because it is divible by the number of its divisors (80).

It is a Smith number, since the sum of its digits (27) coincides with the sum of the digits of its prime factors.

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

It is a nialpdrome in base 16.

It is not an unprimeable number, because it can be changed into a prime (49681) by changing a digit.

49680 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 2149 + ... + 2171.

It is an arithmetic number, because the mean of its divisors is an integer number (2232).

2⁴⁹⁶⁸⁰ is an apocalyptic number.

49680 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 49680, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (89280).

49680 is an abundant number, since it is smaller than the sum of its proper divisors (128880).

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

49680 is a wasteful number, since it uses less digits than its factorization.

49680 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 45 (or 33 counting only the distinct ones).

The product of its (nonzero) digits is 1728, while the sum is 27.

The square root of 49680 is about 222.8901074521. The cubic root of 49680 is about 36.7615540514.

It can be divided in two parts, 496 and 80, that added together give a square (576 = 24²).

The spelling of 49680 in words is "forty-nine thousand, six hundred eighty".