The number 28800

Q: Is 28800 a prime number?

No. 28800 = 2^7 × 3^2 × 5^2, so it is divisible by 2.

28800 is a composite number with 72 divisors. Its prime factorisation is $2^{7}$ × $3^{2}$ × $5^{2}$ . Divisors (72): 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25 … 28800.

Number

Pick any whole number from 1 to 100,000.

28800 = 2^{7} \times 3^{2} \times 5^{2}

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How to work it out

1
What is special about 28800: a Harshad number: divisible by its digit sum 18.
2
28800 is composite. Its prime factorisation is
$28800 = 2^{7} \times 3^{2} \times 5^{2}$
3
The divisors add up to 102765; without 28800 itself that is 73965, so 28800 is abundant (73965 is more than 28800). Euler's totient φ(28800) = 7680 numbers up to 28800 share no factor with it.
4
The digits of 28800 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 59 steps to reach 1.

LaTeX source of the formulas on this page

\[ 28800 = 2^{7} \times 3^{2} \times 5^{2} \]

28800 at a glance

Property	Value
Type	composite
Number of divisors	72
Sum of divisors	102765
Euler totient φ(n)	7680
Square	829440000
Cube	23887872000000
Square root	169.705627 (= 120√2)
Digit sum / digital root	18 / 9
Collatz steps to 1	59
Scientific notation	2.88 × $10^{4}$

28800 in other forms

Form	Value
In words	twenty-eight thousand eight hundred
Binary (base 2)	111000010000000
Octal (base 8)	70200
Hexadecimal (base 16)	7080
Base 3	1110111200
As time	28800 seconds = 8 h 0 min 0 s

Is 28800 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (28800 ÷ 2 = 14400)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (28800 ÷ 3 = 9600)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (28800 ÷ 4 = 7200)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (28800 ÷ 5 = 5760)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (28800 ÷ 6 = 4800)	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 (28800 ÷ 8 = 3600)	A number is divisible by 8 if the last three digits make a multiple of 8.
9	Yes (28800 ÷ 9 = 3200)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (28800 ÷ 10 = 2880)	A number is divisible by 10 if the last digit is 0.
11	No (remainder 2)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (28800 ÷ 12 = 2400)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 28800 a prime number?

No. 28800 = $2^{7}$ × $3^{2}$ × $5^{2}$ , so it is divisible by 2.

What are the factors of 28800?

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 30, 32, 36, 40, 45, 48, 50, 60, 64, 72, 75, 80, 90, 96, 100, 120, 128, 144, 150, 160, 180, 192, 200, 225, 240, 288, 300, 320, 360, 384, 400, 450, 480, 576, 600, 640, 720, 800, 900, 960, 1152, 1200, 1440, 1600, 1800, 1920, 2400, 2880, 3200, 3600, 4800, 5760, 7200, 9600, 14400, 28800.

What is 28800 in binary?

111000010000000 (hexadecimal 7080, octal 70200).

What is the square root of 28800?

About 169.7056, exactly 120√2.

Is 28800 divisible by 3?

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

What is special about the number 28800?

28800 is a Harshad number: divisible by its digit sum 18.