The number 67536

Q: Is 67536 a prime number?

No. 67536 = 2^4 × 3^2 × 7 × 67, so it is divisible by 2.

67536 is a composite number with 60 divisors. Its prime factorisation is $2^{4}$ × $3^{2}$ × 7 × 67. Divisors (60): 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 36 … 67536.

Number

Pick any whole number from 1 to 100,000.

67536 = 2^{4} \times 3^{2} \times 7 \times 67

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How to work it out

1
67536 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
2
67536 is composite. Its prime factorisation is
$67536 = 2^{4} \times 3^{2} \times 7 \times 67$
3
The divisors add up to 219232; without 67536 itself that is 151696, so 67536 is abundant (151696 is more than 67536). Euler's totient φ(67536) = 19008 numbers up to 67536 share no factor with it.
4
The digits of 67536 add up to 27, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 174 steps to reach 1.

LaTeX source of the formulas on this page

\[ 67536 = 2^{4} \times 3^{2} \times 7 \times 67 \]

67536 at a glance

Property	Value
Type	composite
Number of divisors	60
Sum of divisors	219232
Euler totient φ(n)	19008
Square	4561111296
Cube	308039212486656
Square root	259.876894 (= 12√469)
Digit sum / digital root	27 / 9
Collatz steps to 1	174
Scientific notation	6.7536 × $10^{4}$

67536 in other forms

Form	Value
In words	sixty-seven thousand five hundred and thirty-six
Binary (base 2)	10000011111010000
Octal (base 8)	203720
Hexadecimal (base 16)	107D0
Base 3	10102122100
As time	67536 seconds = 18 h 45 min 36 s

Is 67536 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (67536 ÷ 2 = 33768)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (67536 ÷ 3 = 22512)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (67536 ÷ 4 = 16884)	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	Yes (67536 ÷ 6 = 11256)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	Yes (67536 ÷ 7 = 9648)	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 (67536 ÷ 8 = 8442)	A number is divisible by 8 if the last three digits make a multiple of 8.
9	Yes (67536 ÷ 9 = 7504)	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 7)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (67536 ÷ 12 = 5628)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 67536 a prime number?

No. 67536 = $2^{4}$ × $3^{2}$ × 7 × 67, so it is divisible by 2.

What are the factors of 67536?

1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 36, 42, 48, 56, 63, 67, 72, 84, 112, 126, 134, 144, 168, 201, 252, 268, 336, 402, 469, 504, 536, 603, 804, 938, 1008, 1072, 1206, 1407, 1608, 1876, 2412, 2814, 3216, 3752, 4221, 4824, 5628, 7504, 8442, 9648, 11256, 16884, 22512, 33768, 67536.

What is 67536 in binary?

10000011111010000 (hexadecimal 107D0, octal 203720).

What is the square root of 67536?

About 259.8769, exactly 12√469.

Is 67536 divisible by 3?

Yes. Its digits add up to 27, a multiple of 3.

What is special about the number 67536?

It is a composite number with 60 divisors.