The number 33920
33920 is a composite number with 32 divisors. Its prime factorisation is × 5 × 53. Divisors (32): 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 53, 64, 80, 106, 128, 160 … 33920.
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How to work it out
- 1
What is special about 33920: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
33920 is composite. Its prime factorisation is
- 3
The divisors add up to 82620; without 33920 itself that is 48700, so 33920 is abundant (48700 is more than 33920). Euler's totient φ(33920) = 13312 numbers up to 33920 share no factor with it.
- 4
The digits of 33920 add up to 17, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 129 steps to reach 1.
LaTeX source of the formulas on this page
\[ 33920 = 2^{7} \times 5 \times 53 \]33920 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 82620 |
| Euler totient φ(n) | 13312 |
| Square | 1150566400 |
| Cube | 39027212288000 |
| Square root | 184.173831 (= 8√530) |
| Digit sum / digital root | 17 / 8 |
| Collatz steps to 1 | 129 |
| Scientific notation | 3.392 × |
33920 in other forms
| Form | Value |
|---|---|
| In words | thirty-three thousand nine hundred and twenty |
| Binary (base 2) | 1000010010000000 |
| Octal (base 8) | 102200 |
| Hexadecimal (base 16) | 8480 |
| Base 3 | 1201112022 |
| As time | 33920 seconds = 9 h 25 min 20 s |
Is 33920 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (33920 ÷ 2 = 16960) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (33920 ÷ 4 = 8480) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (33920 ÷ 5 = 6784) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 2) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 (33920 ÷ 8 = 4240) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 8) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (33920 ÷ 10 = 3392) | 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 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 33920 a prime number?
No. 33920 = × 5 × 53, so it is divisible by 2.
What are the factors of 33920?
1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 53, 64, 80, 106, 128, 160, 212, 265, 320, 424, 530, 640, 848, 1060, 1696, 2120, 3392, 4240, 6784, 8480, 16960, 33920.
What is 33920 in binary?
1000010010000000 (hexadecimal 8480, octal 102200).
What is the square root of 33920?
About 184.1738, exactly 8√530.
Is 33920 divisible by 3?
No. Its digits add up to 17, which is not a multiple of 3.
What is special about the number 33920?
33920 is a happy number: repeatedly adding the squares of its digits reaches 1.