420768 has 48 divisors (see below), whose sum is σ = 1229760. Its totient is φ = 139968.

The previous prime is 420757. The next prime is 420769. The reversal of 420768 is 867024.

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 (27).

It is not an unprimeable number, because it can be changed into a prime (420769) 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, 621 + ... + 1107.

It is an arithmetic number, because the mean of its divisors is an integer number (25620).

2⁴²⁰⁷⁶⁸ is an apocalyptic number.

420768 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 420768, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (614880).

420768 is an abundant number, since it is smaller than the sum of its proper divisors (808992).

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

420768 is a wasteful number, since it uses less digits than its factorization.

420768 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 506 (or 492 counting only the distinct ones).

The product of its (nonzero) digits is 2688, while the sum is 27.

The square root of 420768 is about 648.6663240835. Note that the first 3 decimals coincide. The cubic root of 420768 is about 74.9343425381.

The spelling of 420768 in words is "four hundred twenty thousand, seven hundred sixty-eight".