72961000 has 96 divisors (see below), whose sum is σ = 198736200. Its totient is φ = 24998400.

The previous prime is 72960997. The next prime is 72961001. The reversal of 72961000 is 16927.

It can be written as a sum of positive squares in 4 ways, for example, as 12152196 + 60808804 = 3486^2 + 7798^2 .

It is a Harshad number since it is a multiple of its sum of digits (25).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (72961001) by changing a digit.

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 23 ways as a sum of consecutive naturals, for example, 48256 + ... + 49744.

Almost surely, 2^72961000 is an apocalyptic number.

72961000 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 72961000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (99368100).

72961000 is an abundant number, since it is smaller than the sum of its proper divisors (125775200).

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

72961000 is a wasteful number, since it uses less digits than its factorization.

72961000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1524 (or 1503 counting only the distinct ones).

The product of its (nonzero) digits is 756, while the sum is 25.

The square root of 72961000 is about 8541.7211380377. The cubic root of 72961000 is about 417.8594797917.

Adding to 72961000 its reverse (16927), we get a palindrome (72977927).

The spelling of 72961000 in words is "seventy-two million, nine hundred sixty-one thousand".