1972 has 12 divisors (see below), whose sum is σ = 3780. Its totient is φ = 896.

The previous prime is 1951. The next prime is 1973. The reversal of 1972 is 2791.

It can be written as a sum of positive squares in 2 ways, for example, as 1296 + 676 = 36^2 + 26^2 .

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (1973) by changing a digit.

1972 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

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, 54 + ... + 82.

It is an arithmetic number, because the mean of its divisors is an integer number (315).

2¹⁹⁷² is an apocalyptic number.

It is an amenable number.

1972 is a deficient number, since it is larger than the sum of its proper divisors (1808).

1972 is a wasteful number, since it uses less digits than its factorization.

1972 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 50 (or 48 counting only the distinct ones).

The product of its digits is 126, while the sum is 19.

The square root of 1972 is about 44.4072066223. The cubic root of 1972 is about 12.5401376463.

Adding to 1972 its sum of digits (19), we get a palindrome (1991).

Subtracting from 1972 its sum of digits (19), we obtain a triangular number (1953 = T₆₂).

It can be divided in two parts, 19 and 72, that added together give a triangular number (91 = T₁₃).

The spelling of 1972 in words is "one thousand, nine hundred seventy-two".