63972 has 18 divisors (see below), whose sum is σ = 161798. Its totient is φ = 21312.

The previous prime is 63949. The next prime is 63977. The reversal of 63972 is 27936.

It can be written as a sum of positive squares in only one way, i.e., 54756 + 9216 = 234^2 + 96^2 .

It is a tau number, because it is divible by the number of its divisors (18).

It is a hoax number, since the sum of its digits (27) coincides with the sum of the digits of its distinct prime factors.

It is not an unprimeable number, because it can be changed into a prime (63977) by changing a digit.

It is a polite number, since it can be written in 5 ways as a sum of consecutive naturals, for example, 853 + ... + 924.

2⁶³⁹⁷² is an apocalyptic number.

It is an amenable number.

63972 is an abundant number, since it is smaller than the sum of its proper divisors (97826).

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

63972 is a wasteful number, since it uses less digits than its factorization.

63972 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 1787 (or 1782 counting only the distinct ones).

The product of its digits is 2268, while the sum is 27.

The square root of 63972 is about 252.9268669003. The cubic root of 63972 is about 39.9941658158.

It can be divided in two parts, 63 and 972, that added together give a triangular number (1035 = T₄₅).

The spelling of 63972 in words is "sixty-three thousand, nine hundred seventy-two".