72206400 has 252 divisors, whose sum is σ = 276471888. Its totient is φ = 16450560.

The previous prime is 72206389. The next prime is 72206411. The reversal of 72206400 is 460227.

It is a happy number.

It is an interprime number because it is at equal distance from previous prime (72206389) and next prime (72206411).

It is a Harshad number since it is a multiple of its sum of digits (21).

It is an unprimeable number.

It is a polite number, since it can be written in 35 ways as a sum of consecutive naturals, for example, 235047 + ... + 235353.

Almost surely, 2^72206400 is an apocalyptic number.

72206400 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 72206400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (138235944).

72206400 is an abundant number, since it is smaller than the sum of its proper divisors (204265488).

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

72206400 is a wasteful number, since it uses less digits than its factorization.

72206400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 346 (or 324 counting only the distinct ones).

The product of its (nonzero) digits is 672, while the sum is 21.

The square root of 72206400 is about 8497.4349070764. The cubic root of 72206400 is about 416.4139124856.

Adding to 72206400 its reverse (460227), we get a palindrome (72666627).

The spelling of 72206400 in words is "seventy-two million, two hundred six thousand, four hundred".