The number 20736

Q: Is 20736 a prime number?

No. 20736 = 2^8 × 3^4, so it is divisible by 2.

Q: What is special about the number 20736?

20736 is a perfect power (12^4); a perfect square (144²); a Harshad number: divisible by its digit sum 18.

20736 is a perfect power ( $12^{4}$ ) and a perfect square (144²). Its prime factorisation is $2^{8}$ × $3^{4}$ . Divisors (45): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54 … 20736.

Number

Pick any whole number from 1 to 100,000.

20736 = 2^{8} \times 3^{4}

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How to work it out

1
What is special about 20736: a perfect power ( $12^{4}$ ); a perfect square (144²); a Harshad number: divisible by its digit sum 18.
2
20736 is composite. Its prime factorisation is
$20736 = 2^{8} \times 3^{4}$
3
The divisors add up to 61831; without 20736 itself that is 41095, so 20736 is abundant (41095 is more than 20736). Euler's totient φ(20736) = 6912 numbers up to 20736 share no factor with it.
4
The digits of 20736 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 30 steps to reach 1.

LaTeX source of the formulas on this page

\[ 20736 = 2^{8} \times 3^{4} \]

20736 at a glance

Property	Value
Type	composite
Number of divisors	45
Sum of divisors	61831
Euler totient φ(n)	6912
Square	429981696
Cube	8916100448256
Square root	144
Digit sum / digital root	18 / 9
Collatz steps to 1	30
Scientific notation	2.0736 × $10^{4}$
Perfect power	$12^{4}$

20736 in other forms

Form	Value
In words	twenty thousand seven hundred and thirty-six
Binary (base 2)	101000100000000
Octal (base 8)	50400
Hexadecimal (base 16)	5100
Base 3	1001110000
As time	20736 seconds = 5 h 45 min 36 s

Is 20736 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (20736 ÷ 2 = 10368)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (20736 ÷ 3 = 6912)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (20736 ÷ 4 = 5184)	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 (20736 ÷ 6 = 3456)	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 (20736 ÷ 8 = 2592)	A number is divisible by 8 if the last three digits make a multiple of 8.
9	Yes (20736 ÷ 9 = 2304)	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 1)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (20736 ÷ 12 = 1728)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 20736 a prime number?

No. 20736 = $2^{8}$ × $3^{4}$ , so it is divisible by 2.

What are the factors of 20736?

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 81, 96, 108, 128, 144, 162, 192, 216, 256, 288, 324, 384, 432, 576, 648, 768, 864, 1152, 1296, 1728, 2304, 2592, 3456, 5184, 6912, 10368, 20736.

What is 20736 in binary?

101000100000000 (hexadecimal 5100, octal 50400).

What is the square root of 20736?

144, because 144 × 144 = 20736.

Is 20736 divisible by 3?

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

What is special about the number 20736?

20736 is a perfect power ( $12^{4}$ ); a perfect square (144²); a Harshad number: divisible by its digit sum 18.