416 has 12 divisors (see below), whose sum is σ = 882. Its totient is φ = 192.

The previous prime is 409. The next prime is 419. The reversal of 416 is 614.

It can be divided in two parts, 4 and 16, that multiplied together give a 6-th power (64 = 2^{6}).

416 is digitally balanced in base 3, because in such base it contains all the possibile digits an equal number of times.

It can be written as a sum of positive squares in only one way, i.e., 400 + 16 = 20^2 + 4^2 .

It is an alternating number because its digits alternate between even and odd.

416 is an undulating number in base 5.

It is a plaindrome in base 7 and base 11.

It is a nialpdrome in base 8.

It is a zygodrome in base 7.

It is a junction number, because it is equal to *n*+sod(*n*) for *n* = 397 and 406.

It is an inconsummate number, since it does not exist a number *n* which divided by its sum of digits gives 416.

It is not an unprimeable number, because it can be changed into a prime (419) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (3) of ones.

It is a polite number, since it can be written as a sum of consecutive naturals, namely, 26 + ... + 38.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 416, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (441).

416 is an abundant number, since it is smaller than the sum of its proper divisors (466).

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

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

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

The sum of its prime factors is 23 (or 15 counting only the distinct ones).

The product of its digits is 24, while the sum is 11.

The square root of 416 is about 20.3960780544. The cubic root of 416 is about 7.4650223136.

The spelling of 416 in words is "four hundred sixteen", and thus it is an aban number.

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