The number 33660

Q: Is 33660 a prime number?

No. 33660 = 2^2 × 3^2 × 5 × 11 × 17, so it is divisible by 2.

33660 is a composite number with 72 divisors. Its prime factorisation is $2^{2}$ × $3^{2}$ × 5 × 11 × 17. Divisors (72): 1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 15, 17, 18, 20, 22, 30 … 33660.

Number

Pick any whole number from 1 to 100,000.

33660 = 2^{2} \times 3^{2} \times 5 \times 11 \times 17

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How to work it out

1
What is special about 33660: a Harshad number: divisible by its digit sum 18.
2
33660 is composite. Its prime factorisation is
$33660 = 2^{2} \times 3^{2} \times 5 \times 11 \times 17$
3
The divisors add up to 117936; without 33660 itself that is 84276, so 33660 is abundant (84276 is more than 33660). Euler's totient φ(33660) = 7680 numbers up to 33660 share no factor with it.
4
The digits of 33660 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 111 steps to reach 1.

LaTeX source of the formulas on this page

\[ 33660 = 2^{2} \times 3^{2} \times 5 \times 11 \times 17 \]

33660 at a glance

Property	Value
Type	composite
Number of divisors	72
Sum of divisors	117936
Euler totient φ(n)	7680
Square	1132995600
Cube	38136631896000
Square root	183.466618 (= 6√935)
Digit sum / digital root	18 / 9
Collatz steps to 1	111
Scientific notation	3.366 × $10^{4}$

33660 in other forms

Form	Value
In words	thirty-three thousand six hundred and sixty
Binary (base 2)	1000001101111100
Octal (base 8)	101574
Hexadecimal (base 16)	837C
Base 3	1201011200
As time	33660 seconds = 9 h 21 min 0 s

Is 33660 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (33660 ÷ 2 = 16830)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (33660 ÷ 3 = 11220)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (33660 ÷ 4 = 8415)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (33660 ÷ 5 = 6732)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (33660 ÷ 6 = 5610)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	No (remainder 4)	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	No (remainder 4)	A number is divisible by 8 if the last three digits make a multiple of 8.
9	Yes (33660 ÷ 9 = 3740)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (33660 ÷ 10 = 3366)	A number is divisible by 10 if the last digit is 0.
11	Yes (33660 ÷ 11 = 3060)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (33660 ÷ 12 = 2805)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 33660 a prime number?

No. 33660 = $2^{2}$ × $3^{2}$ × 5 × 11 × 17, so it is divisible by 2.

What are the factors of 33660?

1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 15, 17, 18, 20, 22, 30, 33, 34, 36, 44, 45, 51, 55, 60, 66, 68, 85, 90, 99, 102, 110, 132, 153, 165, 170, 180, 187, 198, 204, 220, 255, 306, 330, 340, 374, 396, 495, 510, 561, 612, 660, 748, 765, 935, 990, 1020, 1122, 1530, 1683, 1870, 1980, 2244, 2805, 3060, 3366, 3740, 5610, 6732, 8415, 11220, 16830, 33660.

What is 33660 in binary?

1000001101111100 (hexadecimal 837C, octal 101574).

What is the square root of 33660?

About 183.4666, exactly 6√935.

Is 33660 divisible by 3?

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

What is special about the number 33660?

33660 is a Harshad number: divisible by its digit sum 18.