49968 has 30 divisors (see below), whose sum is σ = 140244. Its totient is φ = 16608.

The previous prime is 49957. The next prime is 49991. The reversal of 49968 is 86994.

It is a Harshad number since it is a multiple of its sum of digits (36).

It is a nude number because it is divisible by every one of its digits.

It is a d-powerful number, because it can be written as 4⁷ + 9² + 9³ + 6 + 8⁵ .

It is a nialpdrome in base 16.

It is a zygodrome in base 2.

It is an unprimeable number.

49968 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 5 ways as a sum of consecutive naturals, for example, 30 + ... + 317.

49968 is a Friedman number, since it can be written as 694*9*8, using all its digits and the basic arithmetic operations.

2⁴⁹⁹⁶⁸ is an apocalyptic number.

49968 is a gapful number since it is divisible by the number (48) 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 49968, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (70122).

49968 is an abundant number, since it is smaller than the sum of its proper divisors (90276).

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

49968 is a wasteful number, since it uses less digits than its factorization.

49968 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 361 (or 352 counting only the distinct ones).

The product of its digits is 15552, while the sum is 36.

The square root of 49968 is about 223.5352321224. The cubic root of 49968 is about 36.8324540420.

The spelling of 49968 in words is "forty-nine thousand, nine hundred sixty-eight".