The number 27000

Q: Is 27000 a prime number?

No. 27000 = 2^3 × 3^3 × 5^3, so it is divisible by 2.

Q: What is special about the number 27000?

27000 is a perfect cube (30^3); a Harshad number: divisible by its digit sum 9.

27000 is a perfect cube ( $30^{3}$ ). Its prime factorisation is $2^{3}$ × $3^{3}$ × $5^{3}$ . Divisors (64): 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 25, 27 … 27000.

Number

Pick any whole number from 1 to 100,000.

27000 = 2^{3} \times 3^{3} \times 5^{3}

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How to work it out

1
What is special about 27000: a perfect cube ( $30^{3}$ ); a Harshad number: divisible by its digit sum 9.
2
27000 is composite. Its prime factorisation is
$27000 = 2^{3} \times 3^{3} \times 5^{3}$
3
The divisors add up to 93600; without 27000 itself that is 66600, so 27000 is abundant (66600 is more than 27000). Euler's totient φ(27000) = 7200 numbers up to 27000 share no factor with it.
4
The digits of 27000 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 139 steps to reach 1.

LaTeX source of the formulas on this page

\[ 27000 = 2^{3} \times 3^{3} \times 5^{3} \]

27000 at a glance

Property	Value
Type	composite
Number of divisors	64
Sum of divisors	93600
Euler totient φ(n)	7200
Square	729000000
Cube	19683000000000
Square root	164.316767 (= 30√30)
Digit sum / digital root	9 / 9
Collatz steps to 1	139
Scientific notation	2.7 × $10^{4}$
Perfect power	$30^{3}$

27000 in other forms

Form	Value
In words	twenty-seven thousand
Binary (base 2)	110100101111000
Octal (base 8)	64570
Hexadecimal (base 16)	6978
Base 3	1101001000
As time	27000 seconds = 7 h 30 min 0 s

Is 27000 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (27000 ÷ 2 = 13500)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (27000 ÷ 3 = 9000)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (27000 ÷ 4 = 6750)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (27000 ÷ 5 = 5400)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (27000 ÷ 6 = 4500)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	No (remainder 1)	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 (27000 ÷ 8 = 3375)	A number is divisible by 8 if the last three digits make a multiple of 8.
9	Yes (27000 ÷ 9 = 3000)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (27000 ÷ 10 = 2700)	A number is divisible by 10 if the last digit is 0.
11	No (remainder 6)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (27000 ÷ 12 = 2250)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 27000 a prime number?

No. 27000 = $2^{3}$ × $3^{3}$ × $5^{3}$ , so it is divisible by 2.

What are the factors of 27000?

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 25, 27, 30, 36, 40, 45, 50, 54, 60, 72, 75, 90, 100, 108, 120, 125, 135, 150, 180, 200, 216, 225, 250, 270, 300, 360, 375, 450, 500, 540, 600, 675, 750, 900, 1000, 1080, 1125, 1350, 1500, 1800, 2250, 2700, 3000, 3375, 4500, 5400, 6750, 9000, 13500, 27000.

What is 27000 in binary?

110100101111000 (hexadecimal 6978, octal 64570).

What is the square root of 27000?

About 164.3168, exactly 30√30.

Is 27000 divisible by 3?

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

What is special about the number 27000?

27000 is a perfect cube ( $30^{3}$ ); a Harshad number: divisible by its digit sum 9.