The number 28224

Q: Is 28224 a prime number?

No. 28224 = 2^6 × 3^2 × 7^2, so it is divisible by 2.

28224 is a perfect square (168²). Its prime factorisation is $2^{6}$ × $3^{2}$ × $7^{2}$ . Divisors (63): 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 32 … 28224.

Number

Pick any whole number from 1 to 100,000.

28224 = 2^{6} \times 3^{2} \times 7^{2}

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How to work it out

1
What is special about 28224: a perfect square (168²); a Harshad number: divisible by its digit sum 18.
2
28224 is composite. Its prime factorisation is
$28224 = 2^{6} \times 3^{2} \times 7^{2}$
3
The divisors add up to 94107; without 28224 itself that is 65883, so 28224 is abundant (65883 is more than 28224). Euler's totient φ(28224) = 8064 numbers up to 28224 share no factor with it.
4
The digits of 28224 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 33 steps to reach 1.

LaTeX source of the formulas on this page

\[ 28224 = 2^{6} \times 3^{2} \times 7^{2} \]

28224 at a glance

Property	Value
Type	composite
Number of divisors	63
Sum of divisors	94107
Euler totient φ(n)	8064
Square	796594176
Cube	22483074023424
Square root	168
Digit sum / digital root	18 / 9
Collatz steps to 1	33
Scientific notation	2.8224 × $10^{4}$
Perfect power	$168^{2}$

28224 in other forms

Form	Value
In words	twenty-eight thousand two hundred and twenty-four
Binary (base 2)	110111001000000
Octal (base 8)	67100
Hexadecimal (base 16)	6E40
Base 3	1102201100
As time	28224 seconds = 7 h 50 min 24 s

Is 28224 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (28224 ÷ 2 = 14112)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (28224 ÷ 3 = 9408)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (28224 ÷ 4 = 7056)	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 (28224 ÷ 6 = 4704)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	Yes (28224 ÷ 7 = 4032)	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 (28224 ÷ 8 = 3528)	A number is divisible by 8 if the last three digits make a multiple of 8.
9	Yes (28224 ÷ 9 = 3136)	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	No (remainder 9)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (28224 ÷ 12 = 2352)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 28224 a prime number?

No. 28224 = $2^{6}$ × $3^{2}$ × $7^{2}$ , so it is divisible by 2.

What are the factors of 28224?

1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 32, 36, 42, 48, 49, 56, 63, 64, 72, 84, 96, 98, 112, 126, 144, 147, 168, 192, 196, 224, 252, 288, 294, 336, 392, 441, 448, 504, 576, 588, 672, 784, 882, 1008, 1176, 1344, 1568, 1764, 2016, 2352, 3136, 3528, 4032, 4704, 7056, 9408, 14112, 28224.

What is 28224 in binary?

110111001000000 (hexadecimal 6E40, octal 67100).

What is the square root of 28224?

168, because 168 × 168 = 28224.

Is 28224 divisible by 3?

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

What is special about the number 28224?

28224 is a perfect square (168²); a Harshad number: divisible by its digit sum 18.