The number 72000

Q: Is 72000 a prime number?

No. 72000 = 2^6 × 3^2 × 5^3, so it is divisible by 2.

72000 is a composite number with 84 divisors. Its prime factorisation is $2^{6}$ × $3^{2}$ × $5^{3}$ . Divisors (84): 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25 … 72000.

Number

Pick any whole number from 1 to 100,000.

72000 = 2^{6} \times 3^{2} \times 5^{3}

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How to work it out

1
What is special about 72000: a Harshad number: divisible by its digit sum 9.
2
72000 is composite. Its prime factorisation is
$72000 = 2^{6} \times 3^{2} \times 5^{3}$
3
The divisors add up to 257556; without 72000 itself that is 185556, so 72000 is abundant (185556 is more than 72000). Euler's totient φ(72000) = 19200 numbers up to 72000 share no factor with it.
4
The digits of 72000 add up to 9, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 50 steps to reach 1.

LaTeX source of the formulas on this page

\[ 72000 = 2^{6} \times 3^{2} \times 5^{3} \]

72000 at a glance

Property	Value
Type	composite
Number of divisors	84
Sum of divisors	257556
Euler totient φ(n)	19200
Square	5184000000
Cube	373248000000000
Square root	268.328157 (= 120√5)
Digit sum / digital root	9 / 9
Collatz steps to 1	50
Scientific notation	7.2 × $10^{4}$

72000 in other forms

Form	Value
In words	seventy-two thousand
Binary (base 2)	10001100101000000
Octal (base 8)	214500
Hexadecimal (base 16)	11940
Base 3	10122202200
As time	72000 seconds = 20 h 0 min 0 s

Is 72000 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (72000 ÷ 2 = 36000)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (72000 ÷ 3 = 24000)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (72000 ÷ 4 = 18000)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (72000 ÷ 5 = 14400)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (72000 ÷ 6 = 12000)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	No (remainder 5)	A number is divisible by 7 if double the last digit and subtract it from the rest: the result is a multiple of 7.
8	Yes (72000 ÷ 8 = 9000)	A number is divisible by 8 if the last three digits make a multiple of 8.
9	Yes (72000 ÷ 9 = 8000)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (72000 ÷ 10 = 7200)	A number is divisible by 10 if the last digit is 0.
11	No (remainder 5)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (72000 ÷ 12 = 6000)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 72000 a prime number?

No. 72000 = $2^{6}$ × $3^{2}$ × $5^{3}$ , so it is divisible by 2.

What are the factors of 72000?

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 30, 32, 36, 40, 45, 48, 50, 60, 64, 72, 75, 80, 90, 96, 100, 120, 125, 144, 150, 160, 180, 192, 200, 225, 240, 250, 288, 300, 320, 360, 375, 400, 450, 480, 500, 576, 600, 720, 750, 800, 900, 960, 1000, 1125, 1200, 1440, 1500, 1600, 1800, 2000, 2250, 2400, 2880, 3000, 3600, 4000, 4500, 4800, 6000, 7200, 8000, 9000, 12000, 14400, 18000, 24000, 36000, 72000.

What is 72000 in binary?

10001100101000000 (hexadecimal 11940, octal 214500).

What is the square root of 72000?

About 268.3282, exactly 120√5.

Is 72000 divisible by 3?

Yes. Its digits add up to 9, a multiple of 3.

What is special about the number 72000?

72000 is a Harshad number: divisible by its digit sum 9.