1972000 has 96 divisors (see below), whose sum is σ = 5307120. Its totient is φ = 716800.

The previous prime is 1971967. The next prime is 1972007. The reversal of 1972000 is 2791.

It can be written as a sum of positive squares in 8 ways, for example, as 219024 + 1752976 = 468^2 + 1324^2 .

It is not an unprimeable number, because it can be changed into a prime (1972007) by changing a digit.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 67986 + ... + 68014.

2^1972000 is an apocalyptic number.

1972000 is a gapful number since it is divisible by the number (10) 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 1972000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (2653560).

1972000 is an abundant number, since it is smaller than the sum of its proper divisors (3335120).

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

1972000 is a wasteful number, since it uses less digits than its factorization.

1972000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 71 (or 53 counting only the distinct ones).

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

The square root of 1972000 is about 1404.2791745234. The cubic root of 1972000 is about 125.4013764627.

Adding to 1972000 its reverse (2791), we get a palindrome (1974791).

It can be divided in two parts, 197 and 2000, that added together give a cube (2197 = 13³).

The spelling of 1972000 in words is "one million, nine hundred seventy-two thousand".