The number 23940

Q: Is 23940 a prime number?

No. 23940 = 2^2 × 3^2 × 5 × 7 × 19, so it is divisible by 2.

23940 is a composite number with 72 divisors. Its prime factorisation is $2^{2}$ × $3^{2}$ × 5 × 7 × 19. Divisors (72): 1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 19, 20, 21 … 23940.

Number

Pick any whole number from 1 to 100,000.

23940 = 2^{2} \times 3^{2} \times 5 \times 7 \times 19

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How to work it out

1
What is special about 23940: a Harshad number: divisible by its digit sum 18.
2
23940 is composite. Its prime factorisation is
$23940 = 2^{2} \times 3^{2} \times 5 \times 7 \times 19$
3
The divisors add up to 87360; without 23940 itself that is 63420, so 23940 is abundant (63420 is more than 23940). Euler's totient φ(23940) = 5184 numbers up to 23940 share no factor with it.
4
The digits of 23940 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 95 steps to reach 1.

LaTeX source of the formulas on this page

\[ 23940 = 2^{2} \times 3^{2} \times 5 \times 7 \times 19 \]

23940 at a glance

Property	Value
Type	composite
Number of divisors	72
Sum of divisors	87360
Euler totient φ(n)	5184
Square	573123600
Cube	13720578984000
Square root	154.725563 (= 6√665)
Digit sum / digital root	18 / 9
Collatz steps to 1	95
Scientific notation	2.394 × $10^{4}$

23940 in other forms

Form	Value
In words	twenty-three thousand nine hundred and forty
Binary (base 2)	101110110000100
Octal (base 8)	56604
Hexadecimal (base 16)	5D84
Base 3	1012211200
As time	23940 seconds = 6 h 39 min 0 s

Is 23940 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (23940 ÷ 2 = 11970)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (23940 ÷ 3 = 7980)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (23940 ÷ 4 = 5985)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (23940 ÷ 5 = 4788)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (23940 ÷ 6 = 3990)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	Yes (23940 ÷ 7 = 3420)	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	Yes (23940 ÷ 9 = 2660)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (23940 ÷ 10 = 2394)	A number is divisible by 10 if the last digit is 0.
11	No (remainder 4)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (23940 ÷ 12 = 1995)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 23940 a prime number?

No. 23940 = $2^{2}$ × $3^{2}$ × 5 × 7 × 19, so it is divisible by 2.

What are the factors of 23940?

1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 19, 20, 21, 28, 30, 35, 36, 38, 42, 45, 57, 60, 63, 70, 76, 84, 90, 95, 105, 114, 126, 133, 140, 171, 180, 190, 210, 228, 252, 266, 285, 315, 342, 380, 399, 420, 532, 570, 630, 665, 684, 798, 855, 1140, 1197, 1260, 1330, 1596, 1710, 1995, 2394, 2660, 3420, 3990, 4788, 5985, 7980, 11970, 23940.

What is 23940 in binary?

101110110000100 (hexadecimal 5D84, octal 56604).

What is the square root of 23940?

About 154.7256, exactly 6√665.

Is 23940 divisible by 3?

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

What is special about the number 23940?

23940 is a Harshad number: divisible by its digit sum 18.