The number 33120
33120 is a composite number with 72 divisors. Its prime factorisation is × × 5 × 23. Divisors (72): 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 23, 24 … 33120.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 33120: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 9.
- 2
33120 is composite. Its prime factorisation is
- 3
The divisors add up to 117936; without 33120 itself that is 84816, so 33120 is abundant (84816 is more than 33120). Euler's totient φ(33120) = 8448 numbers up to 33120 share no factor with it.
- 4
The digits of 33120 add up to 9, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 129 steps to reach 1.
LaTeX source of the formulas on this page
\[ 33120 = 2^{5} \times 3^{2} \times 5 \times 23 \]33120 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 72 |
| Sum of divisors | 117936 |
| Euler totient φ(n) | 8448 |
| Square | 1096934400 |
| Cube | 36330467328000 |
| Square root | 181.989011 (= 12√230) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 129 |
| Scientific notation | 3.312 × |
33120 in other forms
| Form | Value |
|---|---|
| In words | thirty-three thousand one hundred and twenty |
| Binary (base 2) | 1000000101100000 |
| Octal (base 8) | 100540 |
| Hexadecimal (base 16) | 8160 |
| Base 3 | 1200102200 |
| As time | 33120 seconds = 9 h 12 min 0 s |
Is 33120 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (33120 ÷ 2 = 16560) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (33120 ÷ 3 = 11040) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (33120 ÷ 4 = 8280) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (33120 ÷ 5 = 6624) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (33120 ÷ 6 = 5520) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 (33120 ÷ 8 = 4140) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (33120 ÷ 9 = 3680) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (33120 ÷ 10 = 3312) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 10) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (33120 ÷ 12 = 2760) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 33120 a prime number?
No. 33120 = × × 5 × 23, so it is divisible by 2.
What are the factors of 33120?
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 23, 24, 30, 32, 36, 40, 45, 46, 48, 60, 69, 72, 80, 90, 92, 96, 115, 120, 138, 144, 160, 180, 184, 207, 230, 240, 276, 288, 345, 360, 368, 414, 460, 480, 552, 690, 720, 736, 828, 920, 1035, 1104, 1380, 1440, 1656, 1840, 2070, 2208, 2760, 3312, 3680, 4140, 5520, 6624, 8280, 11040, 16560, 33120.
What is 33120 in binary?
1000000101100000 (hexadecimal 8160, octal 100540).
What is the square root of 33120?
About 181.9890, exactly 12√230.
Is 33120 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 33120?
33120 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 9.