417027072 has 352 divisors, whose sum is σ = 1452616704. Its totient is φ = 103219200.

The previous prime is 417027071. The next prime is 417027073. The reversal of 417027072 is 270720714.

It is an interprime number because it is at equal distance from previous prime (417027071) and next prime (417027073).

It is a tau number, because it is divible by the number of its divisors (352).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (417027071) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 31 ways as a sum of consecutive naturals, for example, 9698283 + ... + 9698325.

It is an arithmetic number, because the mean of its divisors is an integer number (4126752).

Almost surely, 2^417027072 is an apocalyptic number.

417027072 is a gapful number since it is divisible by the number (42) 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 417027072, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (726308352).

417027072 is an abundant number, since it is smaller than the sum of its proper divisors (1035589632).

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

417027072 is a wasteful number, since it uses less digits than its factorization.

417027072 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 125 (or 107 counting only the distinct ones).

The product of its (nonzero) digits is 5488, while the sum is 30.

The square root of 417027072 is about 20421.2407066760. The cubic root of 417027072 is about 747.1160786550.

Adding to 417027072 its reverse (270720714), we get a palindrome (687747786).

The spelling of 417027072 in words is "four hundred seventeen million, twenty-seven thousand, seventy-two".