The number 27300

Q: Is 27300 a prime number?

No. 27300 = 2^2 × 3 × 5^2 × 7 × 13, so it is divisible by 2.

27300 is a composite number with 72 divisors. Its prime factorisation is $2^{2}$ × 3 × $5^{2}$ × 7 × 13. Divisors (72): 1, 2, 3, 4, 5, 6, 7, 10, 12, 13, 14, 15, 20, 21, 25, 26 … 27300.

Number

Pick any whole number from 1 to 100,000.

27300 = 2^{2} \times 3 \times 5^{2} \times 7 \times 13

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How to work it out

1
What is special about 27300: a Harshad number: divisible by its digit sum 12.
2
27300 is composite. Its prime factorisation is
$27300 = 2^{2} \times 3 \times 5^{2} \times 7 \times 13$
3
The divisors add up to 97216; without 27300 itself that is 69916, so 27300 is abundant (69916 is more than 27300). Euler's totient φ(27300) = 5760 numbers up to 27300 share no factor with it.
4
The digits of 27300 add up to 12, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 121 steps to reach 1.

LaTeX source of the formulas on this page

\[ 27300 = 2^{2} \times 3 \times 5^{2} \times 7 \times 13 \]

27300 at a glance

Property	Value
Type	composite
Number of divisors	72
Sum of divisors	97216
Euler totient φ(n)	5760
Square	745290000
Cube	20346417000000
Square root	165.227116 (= 10√273)
Digit sum / digital root	12 / 3
Collatz steps to 1	121
Scientific notation	2.73 × $10^{4}$

27300 in other forms

Form	Value
In words	twenty-seven thousand three hundred
Binary (base 2)	110101010100100
Octal (base 8)	65244
Hexadecimal (base 16)	6AA4
Base 3	1101110010
As time	27300 seconds = 7 h 35 min 0 s

Is 27300 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (27300 ÷ 2 = 13650)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (27300 ÷ 3 = 9100)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (27300 ÷ 4 = 6825)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (27300 ÷ 5 = 5460)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (27300 ÷ 6 = 4550)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	Yes (27300 ÷ 7 = 3900)	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	No (remainder 3)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (27300 ÷ 10 = 2730)	A number is divisible by 10 if the last digit is 0.
11	No (remainder 9)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (27300 ÷ 12 = 2275)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 27300 a prime number?

No. 27300 = $2^{2}$ × 3 × $5^{2}$ × 7 × 13, so it is divisible by 2.

What are the factors of 27300?

1, 2, 3, 4, 5, 6, 7, 10, 12, 13, 14, 15, 20, 21, 25, 26, 28, 30, 35, 39, 42, 50, 52, 60, 65, 70, 75, 78, 84, 91, 100, 105, 130, 140, 150, 156, 175, 182, 195, 210, 260, 273, 300, 325, 350, 364, 390, 420, 455, 525, 546, 650, 700, 780, 910, 975, 1050, 1092, 1300, 1365, 1820, 1950, 2100, 2275, 2730, 3900, 4550, 5460, 6825, 9100, 13650, 27300.

What is 27300 in binary?

110101010100100 (hexadecimal 6AA4, octal 65244).

What is the square root of 27300?

About 165.2271, exactly 10√273.

Is 27300 divisible by 3?

Yes. Its digits add up to 12, a multiple of 3.

What is special about the number 27300?

27300 is a Harshad number: divisible by its digit sum 12.