49152 has 30 divisors (see below), whose sum is σ = 131068. Its totient is φ = 16384.

The previous prime is 49139. The next prime is 49157. The reversal of 49152 is 25194.

It is a Jordan-Polya number, since it can be written as 4! ⋅ (2!)^{11}.

It is an ABA number since it can be written as A⋅B^{A}, here for A=12, B=2.

Its product of digits (360) is a multiple of the sum of its prime divisors (5).

It is a nialpdrome in base 2, base 4 and base 16.

It is a zygodrome in base 2.

It is not an unprimeable number, because it can be changed into a prime (49157) by changing a digit.

49152 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a pernicious number, because its binary representation contains a prime number (2) of ones.

In principle, a polygon with 49152 sides can be constructed with ruler and compass.

It is a polite number, since it can be written as a sum of consecutive naturals, namely, 16383 + 16384 + 16385.

49152 is a Friedman number, since it can be written as 2^(9+4)*(5+1), using all its digits and the basic arithmetic operations.

2^{49152} 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 49152, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (65534).

49152 is an abundant number, since it is smaller than the sum of its proper divisors (81916).

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

49152 is an frugal number, since it uses more digits than its factorization.

49152 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 31 (or 5 counting only the distinct ones).

The product of its digits is 360, while the sum is 21.

The square root of 49152 is about 221.7025033688. The cubic root of 49152 is about 36.6308557617.

The spelling of 49152 in words is "forty-nine thousand, one hundred fifty-two".

Divisors: 1 2 3 4 6 8 12 16 24 32 48 64 96 128 192 256 384 512 768 1024 1536 2048 3072 4096 6144 8192 12288 16384 24576 49152

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