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448 = 267

• 4482 = 200704 is the smallest square that contains exactly three digits '0' (not at the end).

• 448 can be written using four 4's:

See also 113.
448 has 14 divisors (see below), whose sum is σ = 1016. Its totient is φ = 192.

The previous prime is 443. The next prime is 449. The reversal of 448 is 844.

448 is nontrivially palindromic in base 3.

448 is an esthetic number in base 7, because in such base its adjacent digits differ by 1.

It is a tau number, because it is divible by the number of its divisors (14).

It is a Harshad number since it is a multiple of its sum of digits (16).

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

It is a plaindrome in base 10 and base 11.

It is a nialpdrome in base 2 and base 8.

It is a zygodrome in base 2.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (443) by changing a digit.

448 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 (3) of ones.

It is a polite number, since it can be written as a sum of consecutive naturals, namely, 61 + ... + 67.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 448, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (508).

448 is an abundant number, since it is smaller than the sum of its proper divisors (568).

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

448 is an equidigital number, since it uses as much as digits as its factorization.

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

The sum of its prime factors is 19 (or 9 counting only the distinct ones).

The product of its digits is 128, while the sum is 16.

The square root of 448 is about 21.1660104885. The cubic root of 448 is about 7.6517247311.

Adding to 448 its sum of digits (16), we get a palindrome (464).

448 divided by its sum of digits (16) gives a triangular number (28 = T7).

Adding to 448 its product of digits (128), we get a square (576 = 242).

The spelling of 448 in words is "four hundred forty-eight", and thus it is an aban number.

Divisors: 1 2 4 7 8 14 16 28 32 56 64 112 224 448