972000 has 144 divisors (see below), whose sum is σ = 3577392. Its totient is φ = 259200.

The previous prime is 971989. The next prime is 972001. The reversal of 972000 is 279.

Adding to 972000 its reverse (279), we get a palindrome (972279).

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.

972000 is digitally balanced in base 2, because in such base it contains all the possibile digits an equal number of times.

It is a tau number, because it is divible by the number of its divisors (144).

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

It is a nialpdrome in base 10.

It is a congruent number.

It is an inconsummate number, since it does not exist a number *n* which divided by its sum of digits gives 972000.

It is not an unprimeable number, because it can be changed into a prime (972001) by changing a digit.

972000 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 194398 + ... + 194402.

It is an arithmetic number, because the mean of its divisors is an integer number (24843).

2^{972000} is an apocalyptic number.

972000 is a gapful number since it is divisible by the number (90) 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 972000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1788696).

972000 is an abundant number, since it is smaller than the sum of its proper divisors (2605392).

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

972000 is an equidigital number, since it uses as much as digits as its factorization.

972000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 40 (or 10 counting only the distinct ones).

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

The square root of 972000 is about 985.9006035093. The cubic root of 972000 is about 99.0578174668.

The spelling of 972000 in words is "nine hundred seventy-two thousand".

Divisors: 1 2 3 4 5 6 8 9 10 12 15 16 18 20 24 25 27 30 32 36 40 45 48 50 54 60 72 75 80 81 90 96 100 108 120 125 135 144 150 160 162 180 200 216 225 240 243 250 270 288 300 324 360 375 400 405 432 450 480 486 500 540 600 648 675 720 750 800 810 864 900 972 1000 1080 1125 1200 1215 1296 1350 1440 1500 1620 1800 1944 2000 2025 2160 2250 2400 2430 2592 2700 3000 3240 3375 3600 3888 4000 4050 4320 4500 4860 5400 6000 6075 6480 6750 7200 7776 8100 9000 9720 10125 10800 12000 12150 12960 13500 16200 18000 19440 20250 21600 24300 27000 30375 32400 36000 38880 40500 48600 54000 60750 64800 81000 97200 108000 121500 162000 194400 243000 324000 486000 972000

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