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442368 = 21433
BaseRepresentation
bin1101100000000000000
3211110211000
41230000000
5103123433
613252000
73521463
oct1540000
9743730
10442368
112823a3
12194000
13126474
14b72da
158b113
hex6c000

442368 has 60 divisors (see below), whose sum is σ = 1310680. Its totient is φ = 147456.

The previous prime is 442367. The next prime is 442397. The reversal of 442368 is 863244.

It is a powerful number, because all its prime factors have an exponent greater than 1 and also an Achilles number because it is not a perfect power.

It is a Jordan-Polya number, since it can be written as (4!)3 ⋅ (2!)5.

It is a Harshad number since it is a multiple of its sum of digits (27).

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 not an unprimeable number, because it can be changed into a prime (442363) by changing a digit.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 147455 + 147456 + 147457.

442368 is a Friedman number, since it can be written as (8*(4*3*2)^4)/6, using all its digits and the basic arithmetic operations.

2442368 is an apocalyptic number.

442368 is a gapful number since it is divisible by the number (48) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 442368, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (655340).

442368 is an abundant number, since it is smaller than the sum of its proper divisors (868312).

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

442368 is an frugal number, since it uses more digits than its factorization.

442368 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 37 (or 5 counting only the distinct ones).

The product of its digits is 4608, while the sum is 27.

The square root of 442368 is about 665.1075101064. The cubic root of 442368 is about 76.1952504945.

Multiplying 442368 by its sum of digits (27), we get a square (11943936 = 34562).

442368 divided by its sum of digits (27) gives a 14-th power (16384 = 214).

It can be divided in two parts, 44236 and 8, that added together give a palindrome (44244).

The spelling of 442368 in words is "four hundred forty-two thousand, three hundred sixty-eight".

Divisors: 1 2 3 4 6 8 9 12 16 18 24 27 32 36 48 54 64 72 96 108 128 144 192 216 256 288 384 432 512 576 768 864 1024 1152 1536 1728 2048 2304 3072 3456 4096 4608 6144 6912 8192 9216 12288 13824 16384 18432 24576 27648 36864 49152 55296 73728 110592 147456 221184 442368