The number 23520

Q: Is 23520 a prime number?

No. 23520 = 2^5 × 3 × 5 × 7^2, so it is divisible by 2.

23520 is a composite number with 72 divisors. Its prime factorisation is $2^{5}$ × 3 × 5 × $7^{2}$ . Divisors (72): 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24 … 23520.

Number

Pick any whole number from 1 to 100,000.

23520 = 2^{5} \times 3 \times 5 \times 7^{2}

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How to work it out

1
What is special about 23520: a Harshad number: divisible by its digit sum 12.
2
23520 is composite. Its prime factorisation is
$23520 = 2^{5} \times 3 \times 5 \times 7^{2}$
3
The divisors add up to 86184; without 23520 itself that is 62664, so 23520 is abundant (62664 is more than 23520). Euler's totient φ(23520) = 5376 numbers up to 23520 share no factor with it.
4
The digits of 23520 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 51 steps to reach 1.

LaTeX source of the formulas on this page

\[ 23520 = 2^{5} \times 3 \times 5 \times 7^{2} \]

23520 at a glance

Property	Value
Type	composite
Number of divisors	72
Sum of divisors	86184
Euler totient φ(n)	5376
Square	553190400
Cube	13011038208000
Square root	153.362316 (= 28√30)
Digit sum / digital root	12 / 3
Collatz steps to 1	51
Scientific notation	2.352 × $10^{4}$

23520 in other forms

Form	Value
In words	twenty-three thousand five hundred and twenty
Binary (base 2)	101101111100000
Octal (base 8)	55740
Hexadecimal (base 16)	5BE0
Base 3	1012021010
As time	23520 seconds = 6 h 32 min 0 s

Is 23520 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (23520 ÷ 2 = 11760)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (23520 ÷ 3 = 7840)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (23520 ÷ 4 = 5880)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (23520 ÷ 5 = 4704)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (23520 ÷ 6 = 3920)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	Yes (23520 ÷ 7 = 3360)	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 (23520 ÷ 8 = 2940)	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 (23520 ÷ 10 = 2352)	A number is divisible by 10 if the last digit is 0.
11	No (remainder 2)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (23520 ÷ 12 = 1960)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 23520 a prime number?

No. 23520 = $2^{5}$ × 3 × 5 × $7^{2}$ , so it is divisible by 2.

What are the factors of 23520?

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 28, 30, 32, 35, 40, 42, 48, 49, 56, 60, 70, 80, 84, 96, 98, 105, 112, 120, 140, 147, 160, 168, 196, 210, 224, 240, 245, 280, 294, 336, 392, 420, 480, 490, 560, 588, 672, 735, 784, 840, 980, 1120, 1176, 1470, 1568, 1680, 1960, 2352, 2940, 3360, 3920, 4704, 5880, 7840, 11760, 23520.

What is 23520 in binary?

101101111100000 (hexadecimal 5BE0, octal 55740).

What is the square root of 23520?

About 153.3623, exactly 28√30.

Is 23520 divisible by 3?

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

What is special about the number 23520?

23520 is a Harshad number: divisible by its digit sum 12.