The number 46656

Q: Is 46656 a prime number?

No. 46656 = 2^6 × 3^6, so it is divisible by 2.

Q: What is special about the number 46656?

46656 is a perfect power (6^6); a perfect square (216²); a Harshad number: divisible by its digit sum 27.

46656 is a perfect power ( $6^{6}$ ) and a perfect square (216²). Its prime factorisation is $2^{6}$ × $3^{6}$ . Divisors (49): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54 … 46656.

Number

Pick any whole number from 1 to 100,000.

46656 = 2^{6} \times 3^{6}

Explain it step by step in chat Make a short video of it

How to work it out

1
What is special about 46656: a perfect power ( $6^{6}$ ); a perfect square (216²); a Harshad number: divisible by its digit sum 27.
2
46656 is composite. Its prime factorisation is
$46656 = 2^{6} \times 3^{6}$
3
The divisors add up to 138811; without 46656 itself that is 92155, so 46656 is abundant (92155 is more than 46656). Euler's totient φ(46656) = 15552 numbers up to 46656 share no factor with it.
4
The digits of 46656 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 39 steps to reach 1.

LaTeX source of the formulas on this page

\[ 46656 = 2^{6} \times 3^{6} \]

46656 at a glance

Property	Value
Type	composite
Number of divisors	49
Sum of divisors	138811
Euler totient φ(n)	15552
Square	2176782336
Cube	101559956668416
Square root	216
Digit sum / digital root	27 / 9
Collatz steps to 1	39
Scientific notation	4.6656 × $10^{4}$
Perfect power	$6^{6}$

46656 in other forms

Form	Value
In words	forty-six thousand six hundred and fifty-six
Binary (base 2)	1011011001000000
Octal (base 8)	133100
Hexadecimal (base 16)	B640
Base 3	2101000000
As time	46656 seconds = 12 h 57 min 36 s

Is 46656 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (46656 ÷ 2 = 23328)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (46656 ÷ 3 = 15552)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (46656 ÷ 4 = 11664)	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 (46656 ÷ 6 = 7776)	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 (46656 ÷ 8 = 5832)	A number is divisible by 8 if the last three digits make a multiple of 8.
9	Yes (46656 ÷ 9 = 5184)	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 5)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (46656 ÷ 12 = 3888)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 46656 a prime number?

No. 46656 = $2^{6}$ × $3^{6}$ , so it is divisible by 2.

What are the factors of 46656?

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 81, 96, 108, 144, 162, 192, 216, 243, 288, 324, 432, 486, 576, 648, 729, 864, 972, 1296, 1458, 1728, 1944, 2592, 2916, 3888, 5184, 5832, 7776, 11664, 15552, 23328, 46656.

What is 46656 in binary?

1011011001000000 (hexadecimal B640, octal 133100).

What is the square root of 46656?

216, because 216 × 216 = 46656.

Is 46656 divisible by 3?

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

What is special about the number 46656?

46656 is a perfect power ( $6^{6}$ ); a perfect square (216²); a Harshad number: divisible by its digit sum 27.