782006400 has 480 divisors, whose sum is σ = 3305681280. Its totient is φ = 178329600.

The previous prime is 782006387. The next prime is 782006411. The reversal of 782006400 is 4600287.

It is a tau number, because it is divible by the number of its divisors (480).

It is a super-2 number, since 2×782006400² = 1223068019281920000, which contains 22 as substring.

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

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 59 ways as a sum of consecutive naturals, for example, 1814185 + ... + 1814615.

It is an arithmetic number, because the mean of its divisors is an integer number (6886836).

Almost surely, 2^782006400 is an apocalyptic number.

782006400 is a gapful number since it is divisible by the number (70) 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 782006400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1652840640).

782006400 is an abundant number, since it is smaller than the sum of its proper divisors (2523674880).

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

782006400 is a wasteful number, since it uses less digits than its factorization.

782006400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 474 (or 448 counting only the distinct ones).

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

The square root of 782006400 is about 27964.3773397514. The cubic root of 782006400 is about 921.3050162694.

Adding to 782006400 its reverse (4600287), we get a palindrome (786606687).

The spelling of 782006400 in words is "seven hundred eighty-two million, six thousand, four hundred".