The number 14400

Q: Is 14400 a prime number?

No. 14400 = 2^6 × 3^2 × 5^2, so it is divisible by 2.

14400 is a perfect square (120²). Its prime factorisation is $2^{6}$ × $3^{2}$ × $5^{2}$ . Divisors (63): 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25 … 14400.

Number

Pick any whole number from 1 to 100,000.

14400 = 2^{6} \times 3^{2} \times 5^{2}

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How to work it out

1
What is special about 14400: a perfect square (120²); a Harshad number: divisible by its digit sum 9.
2
14400 is composite. Its prime factorisation is
$14400 = 2^{6} \times 3^{2} \times 5^{2}$
3
The divisors add up to 51181; without 14400 itself that is 36781, so 14400 is abundant (36781 is more than 14400). Euler's totient φ(14400) = 3840 numbers up to 14400 share no factor with it.
4
The digits of 14400 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 58 steps to reach 1.

LaTeX source of the formulas on this page

\[ 14400 = 2^{6} \times 3^{2} \times 5^{2} \]

14400 at a glance

Property	Value
Type	composite
Number of divisors	63
Sum of divisors	51181
Euler totient φ(n)	3840
Square	207360000
Cube	2985984000000
Square root	120
Digit sum / digital root	9 / 9
Collatz steps to 1	58
Scientific notation	1.44 × $10^{4}$
Perfect power	$120^{2}$

14400 in other forms

Form	Value
In words	fourteen thousand four hundred
Binary (base 2)	11100001000000
Octal (base 8)	34100
Hexadecimal (base 16)	3840
Base 3	201202100
As time	14400 seconds = 4 h 0 min 0 s

Is 14400 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (14400 ÷ 2 = 7200)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (14400 ÷ 3 = 4800)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (14400 ÷ 4 = 3600)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (14400 ÷ 5 = 2880)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (14400 ÷ 6 = 2400)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	No (remainder 1)	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 (14400 ÷ 8 = 1800)	A number is divisible by 8 if the last three digits make a multiple of 8.
9	Yes (14400 ÷ 9 = 1600)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (14400 ÷ 10 = 1440)	A number is divisible by 10 if the last digit is 0.
11	No (remainder 1)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (14400 ÷ 12 = 1200)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 14400 a prime number?

No. 14400 = $2^{6}$ × $3^{2}$ × $5^{2}$ , so it is divisible by 2.

What are the factors of 14400?

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, 144, 150, 160, 180, 192, 200, 225, 240, 288, 300, 320, 360, 400, 450, 480, 576, 600, 720, 800, 900, 960, 1200, 1440, 1600, 1800, 2400, 2880, 3600, 4800, 7200, 14400.

What is 14400 in binary?

11100001000000 (hexadecimal 3840, octal 34100).

What is the square root of 14400?

120, because 120 × 120 = 14400.

Is 14400 divisible by 3?

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

What is special about the number 14400?

14400 is a perfect square (120²); a Harshad number: divisible by its digit sum 9.