127968 has 48 divisors (see below), whose sum is σ = 354816. Its totient is φ = 40320.

The previous prime is 127951. The next prime is 127973. The reversal of 127968 is 869721.

It is a tau number, because it is divible by the number of its divisors (48).

It is a zygodrome in base 2.

It is a congruent number.

It is an unprimeable number.

127968 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 7 ways as a sum of consecutive naturals, for example, 2955 + ... + 2997.

It is an arithmetic number, because the mean of its divisors is an integer number (7392).

2¹²⁷⁹⁶⁸ is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 127968, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (177408).

127968 is an abundant number, since it is smaller than the sum of its proper divisors (226848).

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

127968 is a wasteful number, since it uses less digits than its factorization.

127968 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 87 (or 79 counting only the distinct ones).

The product of its digits is 6048, while the sum is 33.

The square root of 127968 is about 357.7261522450. The cubic root of 127968 is about 50.3926419089.

The spelling of 127968 in words is "one hundred twenty-seven thousand, nine hundred sixty-eight".