The number 16200

Q: Is 16200 a prime number?

No. 16200 = 2^3 × 3^4 × 5^2, so it is divisible by 2.

16200 is a composite number with 60 divisors. Its prime factorisation is $2^{3}$ × $3^{4}$ × $5^{2}$ . Divisors (60): 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 25, 27 … 16200.

Number

Pick any whole number from 1 to 100,000.

16200 = 2^{3} \times 3^{4} \times 5^{2}

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How to work it out

1
What is special about 16200: a Harshad number: divisible by its digit sum 9.
2
16200 is composite. Its prime factorisation is
$16200 = 2^{3} \times 3^{4} \times 5^{2}$
3
The divisors add up to 56265; without 16200 itself that is 40065, so 16200 is abundant (40065 is more than 16200). Euler's totient φ(16200) = 4320 numbers up to 16200 share no factor with it.
4
The digits of 16200 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 159 steps to reach 1.

LaTeX source of the formulas on this page

\[ 16200 = 2^{3} \times 3^{4} \times 5^{2} \]

16200 at a glance

Property	Value
Type	composite
Number of divisors	60
Sum of divisors	56265
Euler totient φ(n)	4320
Square	262440000
Cube	4251528000000
Square root	127.279221 (= 90√2)
Digit sum / digital root	9 / 9
Collatz steps to 1	159
Scientific notation	1.62 × $10^{4}$

16200 in other forms

Form	Value
In words	sixteen thousand two hundred
Binary (base 2)	11111101001000
Octal (base 8)	37510
Hexadecimal (base 16)	3F48
Base 3	211020000
As time	16200 seconds = 4 h 30 min 0 s

Is 16200 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (16200 ÷ 2 = 8100)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (16200 ÷ 3 = 5400)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (16200 ÷ 4 = 4050)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (16200 ÷ 5 = 3240)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (16200 ÷ 6 = 2700)	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 (16200 ÷ 8 = 2025)	A number is divisible by 8 if the last three digits make a multiple of 8.
9	Yes (16200 ÷ 9 = 1800)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (16200 ÷ 10 = 1620)	A number is divisible by 10 if the last digit is 0.
11	No (remainder 8)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (16200 ÷ 12 = 1350)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 16200 a prime number?

No. 16200 = $2^{3}$ × $3^{4}$ × $5^{2}$ , so it is divisible by 2.

What are the factors of 16200?

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 25, 27, 30, 36, 40, 45, 50, 54, 60, 72, 75, 81, 90, 100, 108, 120, 135, 150, 162, 180, 200, 216, 225, 270, 300, 324, 360, 405, 450, 540, 600, 648, 675, 810, 900, 1080, 1350, 1620, 1800, 2025, 2700, 3240, 4050, 5400, 8100, 16200.

What is 16200 in binary?

11111101001000 (hexadecimal 3F48, octal 37510).

What is the square root of 16200?

About 127.2792, exactly 90√2.

Is 16200 divisible by 3?

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

What is special about the number 16200?

16200 is a Harshad number: divisible by its digit sum 9.