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16416 = 253319
BaseRepresentation
bin100000000100000
3211112000
410000200
51011131
6204000
765601
oct40040
924460
1016416
1111374
129600
13761a
145da8
154ce6
hex4020

16416 has 48 divisors (see below), whose sum is σ = 50400. Its totient is φ = 5184.

The previous prime is 16411. The next prime is 16417. The reversal of 16416 is 61461.

Adding to 16416 its reverse (61461), we get a palindrome (77877).

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.

Its product of digits (144) is a multiple of the sum of its prime divisors (24).

It is a nialpdrome in base 12.

It is not an unprimeable number, because it can be changed into a prime (16411) by changing a digit.

16416 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.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 855 + ... + 873.

It is an arithmetic number, because the mean of its divisors is an integer number (1050).

216416 is an apocalyptic number.

16416 is a gapful number since it is divisible by the number (16) 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 16416, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (25200).

16416 is an abundant number, since it is smaller than the sum of its proper divisors (33984).

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

16416 is a wasteful number, since it uses less digits than its factorization.

16416 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 38 (or 24 counting only the distinct ones).

The product of its digits is 144, while the sum is 18.

The square root of 16416 is about 128.1249390244. The cubic root of 16416 is about 25.4149415055.

The spelling of 16416 in words is "sixteen thousand, four hundred sixteen".

Divisors: 1 2 3 4 6 8 9 12 16 18 19 24 27 32 36 38 48 54 57 72 76 96 108 114 144 152 171 216 228 288 304 342 432 456 513 608 684 864 912 1026 1368 1824 2052 2736 4104 5472 8208 16416