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107584 = 26412
BaseRepresentation
bin11010010001000000
312110120121
4122101000
511420314
62150024
7625441
oct322100
9173517
10107584
1173914
1252314
1339c79
142b2c8
1521d24
hex1a440

107584 has 21 divisors (see below), whose sum is σ = 218821. Its totient is φ = 52480.

The previous prime is 107581. The next prime is 107599. The reversal of 107584 is 485701.

107584 = T327 + T328.

The square root of 107584 is 328.

It is a perfect power (a square), and thus also a powerful number.

It can be written as a sum of positive squares in only one way, i.e., 5184 + 102400 = 72^2 + 320^2 .

It is a Duffinian number.

It is a nialpdrome in base 8.

It is not an unprimeable number, because it can be changed into a prime (107581) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (5) of ones.

It is a polite number, since it can be written in 2 ways as a sum of consecutive naturals, for example, 2604 + ... + 2644.

107584 is a Friedman number, since it can be written as (8*(40+1))^(7-5), using all its digits and the basic arithmetic operations.

2107584 is an apocalyptic number.

107584 is the 328-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 107584

107584 is an abundant number, since it is smaller than the sum of its proper divisors (111237).

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

107584 is an frugal number, since it uses more digits than its factorization.

107584 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 94 (or 43 counting only the distinct ones).

The product of its (nonzero) digits is 1120, while the sum is 25.

The cubic root of 107584 is about 47.5608085475.

Multiplying 107584 by its sum of digits (25), we get a square (2689600 = 16402).

The spelling of 107584 in words is "one hundred seven thousand, five hundred eighty-four".

Divisors: 1 2 4 8 16 32 41 64 82 164 328 656 1312 1681 2624 3362 6724 13448 26896 53792 107584