42624 has 48 divisors (see below), whose sum is σ = 125970. Its totient is φ = 13824.

The previous prime is 42611. The next prime is 42641.

42624 is a *`hidden beast`* number, since 42 + 624 = 666.

42624 is nontrivially palindromic in base 10.

It can be written as a sum of positive squares in only one way, i.e., 28224 + 14400 = 168^2 + 120^2 .

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

It is a Harshad number since it is a multiple of its sum of digits (18).

It is a nude number because it is divisible by every one of its digits and also a Zuckerman number because it is divisible by the product of its digits.

It is a d-powerful number, because it can be written as **4**^{2} + **2**^{11} + **6**^{5} + **2**^{15} + **4**^{2} .

It is a nialpdrome in base 9.

It is a junction number, because it is equal to *n*+sod(*n*) for *n* = 42597 and 42606.

It is an unprimeable number.

42624 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 (5) of ones.

It is a polite number, since it can be written in 5 ways as a sum of consecutive naturals, for example, 1134 + ... + 1170.

2^{42624} 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 42624, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (62985).

42624 is an abundant number, since it is smaller than the sum of its proper divisors (83346).

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

42624 is a wasteful number, since it uses less digits than its factorization.

With its successor (42625) it forms a Ruth-Aaron pair, since the sum of their prime factors is the same (57).

42624 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 57 (or 42 counting only the distinct ones).

The product of its digits is 384, while the sum is 18.

The square root of 42624 is about 206.4558064090. The cubic root of 42624 is about 34.9315669652.

42624 divided by its product of digits (384) gives a palindrome (111).

It can be divided in two parts, 42 and 624, that added together give a palindrome (666).

The spelling of 42624 in words is "forty-two thousand, six hundred twenty-four".

Divisors: 1 2 3 4 6 8 9 12 16 18 24 32 36 37 48 64 72 74 96 111 128 144 148 192 222 288 296 333 384 444 576 592 666 888 1152 1184 1332 1776 2368 2664 3552 4736 5328 7104 10656 14208 21312 42624

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