The number 39204

Q: Is 39204 a prime number?

No. 39204 = 2^2 × 3^4 × 11^2, so it is divisible by 2.

39204 is a perfect square (198²). Its prime factorisation is $2^{2}$ × $3^{4}$ × $11^{2}$ . Divisors (45): 1, 2, 3, 4, 6, 9, 11, 12, 18, 22, 27, 33, 36, 44, 54, 66 … 39204.

Number

Pick any whole number from 1 to 100,000.

39204 = 2^{2} \times 3^{4} \times 11^{2}

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How to work it out

1
What is special about 39204: a perfect square (198²); a Harshad number: divisible by its digit sum 18.
2
39204 is composite. Its prime factorisation is
$39204 = 2^{2} \times 3^{4} \times 11^{2}$
3
The divisors add up to 112651; without 39204 itself that is 73447, so 39204 is abundant (73447 is more than 39204). Euler's totient φ(39204) = 11880 numbers up to 39204 share no factor with it.
4
The digits of 39204 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 106 steps to reach 1.

LaTeX source of the formulas on this page

\[ 39204 = 2^{2} \times 3^{4} \times 11^{2} \]

39204 at a glance

Property	Value
Type	composite
Number of divisors	45
Sum of divisors	112651
Euler totient φ(n)	11880
Square	1536953616
Cube	60254729561664
Square root	198
Digit sum / digital root	18 / 9
Collatz steps to 1	106
Scientific notation	3.9204 × $10^{4}$
Perfect power	$198^{2}$

39204 in other forms

Form	Value
In words	thirty-nine thousand two hundred and four
Binary (base 2)	1001100100100100
Octal (base 8)	114444
Hexadecimal (base 16)	9924
Base 3	1222210000
As time	39204 seconds = 10 h 53 min 24 s

Is 39204 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (39204 ÷ 2 = 19602)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (39204 ÷ 3 = 13068)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (39204 ÷ 4 = 9801)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	No (remainder 4)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (39204 ÷ 6 = 6534)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	No (remainder 4)	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 (39204 ÷ 9 = 4356)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	No (remainder 4)	A number is divisible by 10 if the last digit is 0.
11	Yes (39204 ÷ 11 = 3564)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (39204 ÷ 12 = 3267)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 39204 a prime number?

No. 39204 = $2^{2}$ × $3^{4}$ × $11^{2}$ , so it is divisible by 2.

What are the factors of 39204?

1, 2, 3, 4, 6, 9, 11, 12, 18, 22, 27, 33, 36, 44, 54, 66, 81, 99, 108, 121, 132, 162, 198, 242, 297, 324, 363, 396, 484, 594, 726, 891, 1089, 1188, 1452, 1782, 2178, 3267, 3564, 4356, 6534, 9801, 13068, 19602, 39204.

What is 39204 in binary?

1001100100100100 (hexadecimal 9924, octal 114444).

What is the square root of 39204?

198, because 198 × 198 = 39204.

Is 39204 divisible by 3?

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

What is special about the number 39204?

39204 is a perfect square (198²); a Harshad number: divisible by its digit sum 18.