451968 has 64 divisors (see below), whose sum is σ = 1321920. Its totient is φ = 135680.

The previous prime is 451967. The next prime is 451987. The reversal of 451968 is 869154.

It is a tau number, because it is divible by the number of its divisors (64).

It is a Harshad number since it is a multiple of its sum of digits (33).

Its product of digits (8640) is a multiple of the sum of its prime factors (135).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (451961) by changing a digit.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 4171 + ... + 4277.

It is an arithmetic number, because the mean of its divisors is an integer number (20655).

2⁴⁵¹⁹⁶⁸ is an apocalyptic number.

451968 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 451968, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (660960).

451968 is an abundant number, since it is smaller than the sum of its proper divisors (869952).

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

451968 is a wasteful number, since it uses less digits than its factorization.

451968 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 135 (or 123 counting only the distinct ones).

The product of its digits is 8640, while the sum is 33.

The square root of 451968 is about 672.2856535729. The cubic root of 451968 is about 76.7424916704.

The spelling of 451968 in words is "four hundred fifty-one thousand, nine hundred sixty-eight".