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138384 = 2432312
BaseRepresentation
bin100001110010010000
321000211100
4201302100
513412014
62544400
71114311
oct416220
9230740
10138384
1194a74
1268100
134acac
1438608
152b009
hex21c90

138384 has 45 divisors (see below), whose sum is σ = 400179. Its totient is φ = 44640.

The previous prime is 138373. The next prime is 138389. The reversal of 138384 is 483831.

Multipling 138384 by its product of digits (2304), we get a square (318836736 = 178562).

138384 = T371 + T372.

The square root of 138384 is 372.

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

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

Its product of digits (2304) is a multiple of the sum of its prime divisors (36).

It is not an unprimeable number, because it can be changed into a prime (138389) by changing a digit.

It is a polite number, since it can be written in 8 ways as a sum of consecutive naturals, for example, 4449 + ... + 4479.

2138384 is an apocalyptic number.

138384 is the 372-nd square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 138384

138384 is an abundant number, since it is smaller than the sum of its proper divisors (261795).

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

138384 is a wasteful number, since it uses less digits than its factorization.

138384 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 76 (or 36 counting only the distinct ones).

The product of its digits is 2304, while the sum is 27.

The cubic root of 138384 is about 51.7243799529.

The spelling of 138384 in words is "one hundred thirty-eight thousand, three hundred eighty-four".

Divisors: 1 2 3 4 6 8 9 12 16 18 24 31 36 48 62 72 93 124 144 186 248 279 372 496 558 744 961 1116 1488 1922 2232 2883 3844 4464 5766 7688 8649 11532 15376 17298 23064 34596 46128 69192 138384