4972 has 12 divisors (see below), whose sum is σ = 9576. Its totient is φ = 2240.

The previous prime is 4969. The next prime is 4973. The reversal of 4972 is 2794.

It is a super-4 number, since 4×4972⁴ = 2444468646298624, which contains 4444 as substring.

It is a Harshad number since it is a multiple of its sum of digits (22).

4972 is an undulating number in base 15.

Its product of digits (504) is a multiple of the sum of its prime divisors (126).

It is a plaindrome in base 13 and base 16.

It is not an unprimeable number, because it can be changed into a prime (4973) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 13 + ... + 100.

It is an arithmetic number, because the mean of its divisors is an integer number (798).

It is an amenable number.

4972 is a deficient number, since it is larger than the sum of its proper divisors (4604).

4972 is a wasteful number, since it uses less digits than its factorization.

4972 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 128 (or 126 counting only the distinct ones).

The product of its digits is 504, while the sum is 22.

The square root of 4972 is about 70.5124102552. The cubic root of 4972 is about 17.0677801465.

Adding to 4972 its sum of digits (22), we get a palindrome (4994).

Subtracting from 4972 its sum of digits (22), we obtain a triangular number (4950 = T₉₉).

Adding to 4972 its product of digits (504), we get a square (5476 = 74²).

It can be divided in two parts, 49 and 72, that added together give a palindrome (121).

The spelling of 4972 in words is "four thousand, nine hundred seventy-two".