The number 33600
33600 is a composite number with 84 divisors. Its prime factorisation is × 3 × × 7. Divisors (84): 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24 … 33600.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 33600: a Harshad number: divisible by its digit sum 12.
- 2
33600 is composite. Its prime factorisation is
- 3
The divisors add up to 125984; without 33600 itself that is 92384, so 33600 is abundant (92384 is more than 33600). Euler's totient φ(33600) = 7680 numbers up to 33600 share no factor with it.
- 4
The digits of 33600 add up to 12, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 36 steps to reach 1.
LaTeX source of the formulas on this page
\[ 33600 = 2^{6} \times 3 \times 5^{2} \times 7 \]33600 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 84 |
| Sum of divisors | 125984 |
| Euler totient φ(n) | 7680 |
| Square | 1128960000 |
| Cube | 37933056000000 |
| Square root | 183.303028 (= 40√21) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 36 |
| Scientific notation | 3.36 × |
33600 in other forms
| Form | Value |
|---|---|
| In words | thirty-three thousand six hundred |
| Binary (base 2) | 1000001101000000 |
| Octal (base 8) | 101500 |
| Hexadecimal (base 16) | 8340 |
| Base 3 | 1201002110 |
| As time | 33600 seconds = 9 h 20 min 0 s |
Is 33600 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (33600 ÷ 2 = 16800) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (33600 ÷ 3 = 11200) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (33600 ÷ 4 = 8400) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (33600 ÷ 5 = 6720) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (33600 ÷ 6 = 5600) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (33600 ÷ 7 = 4800) | 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 (33600 ÷ 8 = 4200) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (33600 ÷ 10 = 3360) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (33600 ÷ 12 = 2800) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 33600 a prime number?
No. 33600 = × 3 × × 7, so it is divisible by 2.
What are the factors of 33600?
1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 25, 28, 30, 32, 35, 40, 42, 48, 50, 56, 60, 64, 70, 75, 80, 84, 96, 100, 105, 112, 120, 140, 150, 160, 168, 175, 192, 200, 210, 224, 240, 280, 300, 320, 336, 350, 400, 420, 448, 480, 525, 560, 600, 672, 700, 800, 840, 960, 1050, 1120, 1200, 1344, 1400, 1600, 1680, 2100, 2240, 2400, 2800, 3360, 4200, 4800, 5600, 6720, 8400, 11200, 16800, 33600.
What is 33600 in binary?
1000001101000000 (hexadecimal 8340, octal 101500).
What is the square root of 33600?
About 183.3030, exactly 40√21.
Is 33600 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 33600?
33600 is a Harshad number: divisible by its digit sum 12.