The number 72900

Q: Is 72900 a prime number?

No. 72900 = 2^2 × 3^6 × 5^2, so it is divisible by 2.

72900 is a perfect square (270²). Its prime factorisation is $2^{2}$ × $3^{6}$ × $5^{2}$ . Divisors (63): 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 27, 30, 36 … 72900.

Number

Pick any whole number from 1 to 100,000.

72900 = 2^{2} \times 3^{6} \times 5^{2}

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How to work it out

1
What is special about 72900: a perfect square (270²); a Harshad number: divisible by its digit sum 18.
2
72900 is composite. Its prime factorisation is
$72900 = 2^{2} \times 3^{6} \times 5^{2}$
3
The divisors add up to 237181; without 72900 itself that is 164281, so 72900 is abundant (164281 is more than 72900). Euler's totient φ(72900) = 19440 numbers up to 72900 share no factor with it.
4
The digits of 72900 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 63 steps to reach 1.

LaTeX source of the formulas on this page

\[ 72900 = 2^{2} \times 3^{6} \times 5^{2} \]

72900 at a glance

Property	Value
Type	composite
Number of divisors	63
Sum of divisors	237181
Euler totient φ(n)	19440
Square	5314410000
Cube	387420489000000
Square root	270
Digit sum / digital root	18 / 9
Collatz steps to 1	63
Scientific notation	7.29 × $10^{4}$
Perfect power	$270^{2}$

72900 in other forms

Form	Value
In words	seventy-two thousand nine hundred
Binary (base 2)	10001110011000100
Octal (base 8)	216304
Hexadecimal (base 16)	11CC4
Base 3	10201000000
As time	72900 seconds = 20 h 15 min 0 s

Is 72900 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (72900 ÷ 2 = 36450)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (72900 ÷ 3 = 24300)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (72900 ÷ 4 = 18225)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (72900 ÷ 5 = 14580)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (72900 ÷ 6 = 12150)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	No (remainder 2)	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	No (remainder 4)	A number is divisible by 8 if the last three digits make a multiple of 8.
9	Yes (72900 ÷ 9 = 8100)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (72900 ÷ 10 = 7290)	A number is divisible by 10 if the last digit is 0.
11	No (remainder 3)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (72900 ÷ 12 = 6075)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 72900 a prime number?

No. 72900 = $2^{2}$ × $3^{6}$ × $5^{2}$ , so it is divisible by 2.

What are the factors of 72900?

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 27, 30, 36, 45, 50, 54, 60, 75, 81, 90, 100, 108, 135, 150, 162, 180, 225, 243, 270, 300, 324, 405, 450, 486, 540, 675, 729, 810, 900, 972, 1215, 1350, 1458, 1620, 2025, 2430, 2700, 2916, 3645, 4050, 4860, 6075, 7290, 8100, 12150, 14580, 18225, 24300, 36450, 72900.

What is 72900 in binary?

10001110011000100 (hexadecimal 11CC4, octal 216304).

What is the square root of 72900?

270, because 270 × 270 = 72900.

Is 72900 divisible by 3?

Yes. Its digits add up to 18, a multiple of 3.

What is special about the number 72900?

72900 is a perfect square (270²); a Harshad number: divisible by its digit sum 18.