416421200 has 120 divisors (see below), whose sum is σ = 1093164408. Its totient is φ = 151511040.

The previous prime is 416421191. The next prime is 416421211. The reversal of 416421200 is 2124614.

It can be written as a sum of positive squares in 12 ways, for example, as 217385536 + 199035664 = 14744^2 + 14108^2 .

It is a Harshad number since it is a multiple of its sum of digits (20).

It is a congruent number.

It is an unprimeable number.

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 23 ways as a sum of consecutive naturals, for example, 379052 + ... + 380148.

Almost surely, 2^416421200 is an apocalyptic number.

416421200 is a gapful number since it is divisible by the number (40) 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 416421200, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (546582204).

416421200 is an abundant number, since it is smaller than the sum of its proper divisors (676743208).

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

416421200 is a wasteful number, since it uses less digits than its factorization.

416421200 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1201 (or 1190 counting only the distinct ones).

The product of its (nonzero) digits is 384, while the sum is 20.

The square root of 416421200 is about 20406.4009565626. The cubic root of 416421200 is about 746.7540908831.

Adding to 416421200 its reverse (2124614), we get a palindrome (418545814).

The spelling of 416421200 in words is "four hundred sixteen million, four hundred twenty-one thousand, two hundred".