The number 65536

Q: Is 65536 a prime number?

No. 65536 = 2^16, so it is divisible by 2.

Q: What is special about the number 65536?

65536 is a power of 2 (2^16); a perfect square (256²).

65536 is a power of 2 ( $2^{16}$ ) and a perfect square (256²). Its prime factorisation is $2^{16}$ . Divisors (17): 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768 … 65536.

Number

Pick any whole number from 1 to 100,000.

65536 = 2^{16}

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How to work it out

1
What is special about 65536: a power of 2 ( $2^{16}$ ); a perfect square (256²).
2
65536 is composite. Its prime factorisation is
$65536 = 2^{16}$
3
The divisors add up to 131071; without 65536 itself that is 65535, so 65536 is deficient (65535 is less than 65536). Euler's totient φ(65536) = 32768 numbers up to 65536 share no factor with it.
4
The digits of 65536 add up to 25, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 16 steps to reach 1.

LaTeX source of the formulas on this page

\[ 65536 = 2^{16} \]

65536 at a glance

Property	Value
Type	composite
Number of divisors	17
Sum of divisors	131071
Euler totient φ(n)	32768
Square	4294967296
Cube	281474976710656
Square root	256
Digit sum / digital root	25 / 7
Collatz steps to 1	16
Scientific notation	6.5536 × $10^{4}$
Perfect power	$2^{16}$

65536 in other forms

Form	Value
In words	sixty-five thousand five hundred and thirty-six
Binary (base 2)	10000000000000000
Octal (base 8)	200000
Hexadecimal (base 16)	10000
Base 3	10022220021
As time	65536 seconds = 18 h 12 min 16 s

Is 65536 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (65536 ÷ 2 = 32768)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	No (remainder 1)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (65536 ÷ 4 = 16384)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	No (remainder 1)	A number is divisible by 5 if the last digit is 0 or 5.
6	No (remainder 4)	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 (65536 ÷ 8 = 8192)	A number is divisible by 8 if the last three digits make a multiple of 8.
9	No (remainder 7)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	No (remainder 6)	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	No (remainder 4)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 65536 a prime number?

No. 65536 = $2^{16}$ , so it is divisible by 2.

What are the factors of 65536?

1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536.

What is 65536 in binary?

10000000000000000 (hexadecimal 10000, octal 200000).

What is the square root of 65536?

256, because 256 × 256 = 65536.

Is 65536 divisible by 3?

No. Its digits add up to 25, which is not a multiple of 3.

What is special about the number 65536?

65536 is a power of 2 ( $2^{16}$ ); a perfect square (256²).