The number 19800

Q: Is 19800 a prime number?

No. 19800 = 2^3 × 3^2 × 5^2 × 11, so it is divisible by 2.

19800 is a composite number with 72 divisors. Its prime factorisation is $2^{3}$ × $3^{2}$ × $5^{2}$ × 11. Divisors (72): 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 15, 18, 20, 22, 24 … 19800.

Number

Pick any whole number from 1 to 100,000.

19800 = 2^{3} \times 3^{2} \times 5^{2} \times 11

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How to work it out

1
What is special about 19800: a Harshad number: divisible by its digit sum 18.
2
19800 is composite. Its prime factorisation is
$19800 = 2^{3} \times 3^{2} \times 5^{2} \times 11$
3
The divisors add up to 72540; without 19800 itself that is 52740, so 19800 is abundant (52740 is more than 19800). Euler's totient φ(19800) = 4800 numbers up to 19800 share no factor with it.
4
The digits of 19800 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 74 steps to reach 1.

LaTeX source of the formulas on this page

\[ 19800 = 2^{3} \times 3^{2} \times 5^{2} \times 11 \]

19800 at a glance

Property	Value
Type	composite
Number of divisors	72
Sum of divisors	72540
Euler totient φ(n)	4800
Square	392040000
Cube	7762392000000
Square root	140.712473 (= 30√22)
Digit sum / digital root	18 / 9
Collatz steps to 1	74
Scientific notation	1.98 × $10^{4}$

19800 in other forms

Form	Value
In words	nineteen thousand eight hundred
Binary (base 2)	100110101011000
Octal (base 8)	46530
Hexadecimal (base 16)	4D58
Base 3	1000011100
As time	19800 seconds = 5 h 30 min 0 s

Is 19800 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (19800 ÷ 2 = 9900)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (19800 ÷ 3 = 6600)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (19800 ÷ 4 = 4950)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (19800 ÷ 5 = 3960)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (19800 ÷ 6 = 3300)	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	Yes (19800 ÷ 8 = 2475)	A number is divisible by 8 if the last three digits make a multiple of 8.
9	Yes (19800 ÷ 9 = 2200)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (19800 ÷ 10 = 1980)	A number is divisible by 10 if the last digit is 0.
11	Yes (19800 ÷ 11 = 1800)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (19800 ÷ 12 = 1650)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 19800 a prime number?

No. 19800 = $2^{3}$ × $3^{2}$ × $5^{2}$ × 11, so it is divisible by 2.

What are the factors of 19800?

1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 15, 18, 20, 22, 24, 25, 30, 33, 36, 40, 44, 45, 50, 55, 60, 66, 72, 75, 88, 90, 99, 100, 110, 120, 132, 150, 165, 180, 198, 200, 220, 225, 264, 275, 300, 330, 360, 396, 440, 450, 495, 550, 600, 660, 792, 825, 900, 990, 1100, 1320, 1650, 1800, 1980, 2200, 2475, 3300, 3960, 4950, 6600, 9900, 19800.

What is 19800 in binary?

100110101011000 (hexadecimal 4D58, octal 46530).

What is the square root of 19800?

About 140.7125, exactly 30√22.

Is 19800 divisible by 3?

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

What is special about the number 19800?

19800 is a Harshad number: divisible by its digit sum 18.