416772 has 48 divisors (see below), whose sum is σ = 1149120. Its totient is φ = 130176.

The previous prime is 416761. The next prime is 416797. The reversal of 416772 is 277614.

It is a Harshad number since it is a multiple of its sum of digits (27).

It is a congruent number.

It is an unprimeable number.

416772 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 (7) of ones.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 1723 + ... + 1949.

It is an arithmetic number, because the mean of its divisors is an integer number (23940).

2⁴¹⁶⁷⁷² is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 416772, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (574560).

416772 is an abundant number, since it is smaller than the sum of its proper divisors (732348).

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

416772 is a wasteful number, since it uses less digits than its factorization.

416772 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 257 (or 249 counting only the distinct ones).

The product of its digits is 2352, while the sum is 27.

The square root of 416772 is about 645.5788100612. The cubic root of 416772 is about 74.6963724630.

The spelling of 416772 in words is "four hundred sixteen thousand, seven hundred seventy-two".