The number 27720

Q: Is 27720 a prime number?

No. 27720 = 2^3 × 3^2 × 5 × 7 × 11, so it is divisible by 2.

27720 is a highly composite number: it has 96 divisors, more than any smaller number. Its prime factorisation is $2^{3}$ × $3^{2}$ × 5 × 7 × 11. Divisors (96): 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 18, 20 … 27720.

Number

Pick any whole number from 1 to 100,000.

27720 = 2^{3} \times 3^{2} \times 5 \times 7 \times 11

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How to work it out

1
What is special about 27720: a highly composite number: it has 96 divisors, more than any smaller number; a Harshad number: divisible by its digit sum 18.
2
27720 is composite. Its prime factorisation is
$27720 = 2^{3} \times 3^{2} \times 5 \times 7 \times 11$
3
The divisors add up to 112320; without 27720 itself that is 84600, so 27720 is abundant (84600 is more than 27720). Euler's totient φ(27720) = 5760 numbers up to 27720 share no factor with it.
4
The digits of 27720 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 152 steps to reach 1.

LaTeX source of the formulas on this page

\[ 27720 = 2^{3} \times 3^{2} \times 5 \times 7 \times 11 \]

27720 at a glance

Property	Value
Type	composite
Number of divisors	96
Sum of divisors	112320
Euler totient φ(n)	5760
Square	768398400
Cube	21300003648000
Square root	166.493243 (= 6√770)
Digit sum / digital root	18 / 9
Collatz steps to 1	152
Scientific notation	2.772 × $10^{4}$

27720 in other forms

Form	Value
In words	twenty-seven thousand seven hundred and twenty
Binary (base 2)	110110001001000
Octal (base 8)	66110
Hexadecimal (base 16)	6C48
Base 3	1102000200
As time	27720 seconds = 7 h 42 min 0 s

Is 27720 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (27720 ÷ 2 = 13860)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (27720 ÷ 3 = 9240)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (27720 ÷ 4 = 6930)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (27720 ÷ 5 = 5544)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (27720 ÷ 6 = 4620)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	Yes (27720 ÷ 7 = 3960)	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 (27720 ÷ 8 = 3465)	A number is divisible by 8 if the last three digits make a multiple of 8.
9	Yes (27720 ÷ 9 = 3080)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (27720 ÷ 10 = 2772)	A number is divisible by 10 if the last digit is 0.
11	Yes (27720 ÷ 11 = 2520)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (27720 ÷ 12 = 2310)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 27720 a prime number?

No. 27720 = $2^{3}$ × $3^{2}$ × 5 × 7 × 11, so it is divisible by 2.

What are the factors of 27720?

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 18, 20, 21, 22, 24, 28, 30, 33, 35, 36, 40, 42, 44, 45, 55, 56, 60, 63, 66, 70, 72, 77, 84, 88, 90, 99, 105, 110, 120, 126, 132, 140, 154, 165, 168, 180, 198, 210, 220, 231, 252, 264, 280, 308, 315, 330, 360, 385, 396, 420, 440, 462, 495, 504, 616, 630, 660, 693, 770, 792, 840, 924, 990, 1155, 1260, 1320, 1386, 1540, 1848, 1980, 2310, 2520, 2772, 3080, 3465, 3960, 4620, 5544, 6930, 9240, 13860, 27720.

What is 27720 in binary?

110110001001000 (hexadecimal 6C48, octal 66110).

What is the square root of 27720?

About 166.4932, exactly 6√770.

Is 27720 divisible by 3?

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

What is special about the number 27720?

27720 is a highly composite number: it has 96 divisors, more than any smaller number; a Harshad number: divisible by its digit sum 18.