The number 23760

Q: Is 23760 a prime number?

No. 23760 = 2^4 × 3^3 × 5 × 11, so it is divisible by 2.

23760 is a composite number with 80 divisors. Its prime factorisation is $2^{4}$ × $3^{3}$ × 5 × 11. Divisors (80): 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 15, 16, 18, 20, 22 … 23760.

Number

Pick any whole number from 1 to 100,000.

23760 = 2^{4} \times 3^{3} \times 5 \times 11

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How to work it out

1
What is special about 23760: a Harshad number: divisible by its digit sum 18.
2
23760 is composite. Its prime factorisation is
$23760 = 2^{4} \times 3^{3} \times 5 \times 11$
3
The divisors add up to 89280; without 23760 itself that is 65520, so 23760 is abundant (65520 is more than 23760). Euler's totient φ(23760) = 5760 numbers up to 23760 share no factor with it.
4
The digits of 23760 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 51 steps to reach 1.

LaTeX source of the formulas on this page

\[ 23760 = 2^{4} \times 3^{3} \times 5 \times 11 \]

23760 at a glance

Property	Value
Type	composite
Number of divisors	80
Sum of divisors	89280
Euler totient φ(n)	5760
Square	564537600
Cube	13413413376000
Square root	154.142791 (= 12√165)
Digit sum / digital root	18 / 9
Collatz steps to 1	51
Scientific notation	2.376 × $10^{4}$

23760 in other forms

Form	Value
In words	twenty-three thousand seven hundred and sixty
Binary (base 2)	101110011010000
Octal (base 8)	56320
Hexadecimal (base 16)	5CD0
Base 3	1012121000
As time	23760 seconds = 6 h 36 min 0 s

Is 23760 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (23760 ÷ 2 = 11880)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (23760 ÷ 3 = 7920)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (23760 ÷ 4 = 5940)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (23760 ÷ 5 = 4752)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (23760 ÷ 6 = 3960)	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	Yes (23760 ÷ 8 = 2970)	A number is divisible by 8 if the last three digits make a multiple of 8.
9	Yes (23760 ÷ 9 = 2640)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (23760 ÷ 10 = 2376)	A number is divisible by 10 if the last digit is 0.
11	Yes (23760 ÷ 11 = 2160)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (23760 ÷ 12 = 1980)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 23760 a prime number?

No. 23760 = $2^{4}$ × $3^{3}$ × 5 × 11, so it is divisible by 2.

What are the factors of 23760?

1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 15, 16, 18, 20, 22, 24, 27, 30, 33, 36, 40, 44, 45, 48, 54, 55, 60, 66, 72, 80, 88, 90, 99, 108, 110, 120, 132, 135, 144, 165, 176, 180, 198, 216, 220, 240, 264, 270, 297, 330, 360, 396, 432, 440, 495, 528, 540, 594, 660, 720, 792, 880, 990, 1080, 1188, 1320, 1485, 1584, 1980, 2160, 2376, 2640, 2970, 3960, 4752, 5940, 7920, 11880, 23760.

What is 23760 in binary?

101110011010000 (hexadecimal 5CD0, octal 56320).

What is the square root of 23760?

About 154.1428, exactly 12√165.

Is 23760 divisible by 3?

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

What is special about the number 23760?

23760 is a Harshad number: divisible by its digit sum 18.