72772128 has 384 divisors, whose sum is σ = 270950400. Its totient is φ = 18662400.

The previous prime is 72772123. The next prime is 72772153. The reversal of 72772128 is 82127727.

It is a super-2 number, since 2×72772128² = 10591565227296768, which contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (36).

It is a junction number, because it is equal to n+sod(n) for n = 72772092 and 72772101.

It is not an unprimeable number, because it can be changed into a prime (72772123) by changing a digit.

It is a polite number, since it can be written in 63 ways as a sum of consecutive naturals, for example, 2347473 + ... + 2347503.

It is an arithmetic number, because the mean of its divisors is an integer number (705600).

Almost surely, 2^72772128 is an apocalyptic number.

72772128 is a gapful number since it is divisible by the number (78) 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 72772128, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (135475200).

72772128 is an abundant number, since it is smaller than the sum of its proper divisors (198178272).

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

72772128 is a wasteful number, since it uses less digits than its factorization.

72772128 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 93 (or 79 counting only the distinct ones).

The product of its digits is 21952, while the sum is 36.

The square root of 72772128 is about 8530.6581223256. The cubic root of 72772128 is about 417.4986013555.

It can be divided in two parts, 72772 and 128, that added together give a square (72900 = 270²).

The spelling of 72772128 in words is "seventy-two million, seven hundred seventy-two thousand, one hundred twenty-eight".