The number 23400

Q: Is 23400 a prime number?

No. 23400 = 2^3 × 3^2 × 5^2 × 13, so it is divisible by 2.

23400 is a composite number with 72 divisors. Its prime factorisation is $2^{3}$ × $3^{2}$ × $5^{2}$ × 13. Divisors (72): 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 15, 18, 20, 24, 25 … 23400.

Number

Pick any whole number from 1 to 100,000.

23400 = 2^{3} \times 3^{2} \times 5^{2} \times 13

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How to work it out

1
What is special about 23400: a Harshad number: divisible by its digit sum 9.
2
23400 is composite. Its prime factorisation is
$23400 = 2^{3} \times 3^{2} \times 5^{2} \times 13$
3
The divisors add up to 84630; without 23400 itself that is 61230, so 23400 is abundant (61230 is more than 23400). Euler's totient φ(23400) = 5760 numbers up to 23400 share no factor with it.
4
The digits of 23400 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 144 steps to reach 1.

LaTeX source of the formulas on this page

\[ 23400 = 2^{3} \times 3^{2} \times 5^{2} \times 13 \]

23400 at a glance

Property	Value
Type	composite
Number of divisors	72
Sum of divisors	84630
Euler totient φ(n)	5760
Square	547560000
Cube	12812904000000
Square root	152.970585 (= 30√26)
Digit sum / digital root	9 / 9
Collatz steps to 1	144
Scientific notation	2.34 × $10^{4}$

23400 in other forms

Form	Value
In words	twenty-three thousand four hundred
Binary (base 2)	101101101101000
Octal (base 8)	55550
Hexadecimal (base 16)	5B68
Base 3	1012002200
As time	23400 seconds = 6 h 30 min 0 s

Is 23400 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (23400 ÷ 2 = 11700)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (23400 ÷ 3 = 7800)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (23400 ÷ 4 = 5850)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (23400 ÷ 5 = 4680)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (23400 ÷ 6 = 3900)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	No (remainder 6)	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 (23400 ÷ 8 = 2925)	A number is divisible by 8 if the last three digits make a multiple of 8.
9	Yes (23400 ÷ 9 = 2600)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (23400 ÷ 10 = 2340)	A number is divisible by 10 if the last digit is 0.
11	No (remainder 3)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (23400 ÷ 12 = 1950)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 23400 a prime number?

No. 23400 = $2^{3}$ × $3^{2}$ × $5^{2}$ × 13, so it is divisible by 2.

What are the factors of 23400?

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 15, 18, 20, 24, 25, 26, 30, 36, 39, 40, 45, 50, 52, 60, 65, 72, 75, 78, 90, 100, 104, 117, 120, 130, 150, 156, 180, 195, 200, 225, 234, 260, 300, 312, 325, 360, 390, 450, 468, 520, 585, 600, 650, 780, 900, 936, 975, 1170, 1300, 1560, 1800, 1950, 2340, 2600, 2925, 3900, 4680, 5850, 7800, 11700, 23400.

What is 23400 in binary?

101101101101000 (hexadecimal 5B68, octal 55550).

What is the square root of 23400?

About 152.9706, exactly 30√26.

Is 23400 divisible by 3?

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

What is special about the number 23400?

23400 is a Harshad number: divisible by its digit sum 9.