• 672 can be written using four 4's:

672 has 24 divisors (see below), whose sum is σ = 2016. Its totient is φ = 192.

The previous prime is 661. The next prime is 673. The reversal of 672 is 276.

It is a tau number, because it is divible by the number of its divisors (24).

It is a harmonic number, since the harmonic mean of its divisors is an integer.

672 is an admirable number.

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

It is one of the 548 Lynch-Bell numbers.

Its product of digits (84) is a multiple of the sum of its prime divisors (12).

It is a nialpdrome in base 4.

It is a zygodrome in base 4.

It is not an unprimeable number, because it can be changed into a prime (673) 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 in 3 ways as a sum of consecutive naturals, for example, 93 + ... + 99.

It is an arithmetic number, because the mean of its divisors is an integer number (84).

672 is a droll number since its even prime factors and its odd prime factors have the same sum.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 672, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1008).

672 is an abundant number, since it is smaller than the sum of its proper divisors (1344).

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

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

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

The sum of its prime factors is 20 (or 12 counting only the distinct ones).

The product of its digits is 84, while the sum is 15.

The square root of 672 is about 25.9229627936. The cubic root of 672 is about 8.7590382798.

It can be divided in two parts, 6 and 72, that added together give a triangular number (78 = T_{12}).

The spelling of 672 in words is "six hundred seventy-two", and thus it is an aban number.

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