• 972 can be written using four 4's:

972 has 18 divisors (see below), whose sum is σ = 2548. Its totient is φ = 324.

The previous prime is 971. The next prime is 977. The reversal of 972 is 279.

It is a powerful number, because all its prime factors have an exponent greater than 1 and also an Achilles number because it is not a perfect power.

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

It is a Harshad number since it is a multiple of its sum of digits (18).

It is a plaindrome in base 7, base 13, base 15 and base 16.

It is a nialpdrome in base 3, base 6 and base 10.

It is a zygodrome in base 2 and base 3.

It is an inconsummate number, since it does not exist a number *n* which divided by its sum of digits gives 972.

It is not an unprimeable number, because it can be changed into a prime (971) 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, 323 + 324 + 325.

2^{972} is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 972, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1274).

972 is an abundant number, since it is smaller than the sum of its proper divisors (1576).

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

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

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

The sum of its prime factors is 19 (or 5 counting only the distinct ones).

The product of its digits is 126, while the sum is 18.

The square root of 972 is about 31.1769145362. The cubic root of 972 is about 9.9057817467.

Adding to 972 its sum of digits (18), we get a triangular number (990 = T_{44}).

It can be divided in two parts, 97 and 2, that added together give a palindrome (99).

The spelling of 972 in words is "nine hundred seventy-two", and thus it is an aban number.

• e-mail: info -at- numbersaplenty.com • Privacy notice • done in 0.144 sec. • engine limits •