The number 33900
33900 is a composite number with 36 divisors. Its prime factorisation is × 3 × × 113. Divisors (36): 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100 … 33900.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 33900: a Harshad number: divisible by its digit sum 15.
- 2
33900 is composite. Its prime factorisation is
- 3
The divisors add up to 98952; without 33900 itself that is 65052, so 33900 is abundant (65052 is more than 33900). Euler's totient φ(33900) = 8960 numbers up to 33900 share no factor with it.
- 4
The digits of 33900 add up to 15, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 111 steps to reach 1.
LaTeX source of the formulas on this page
\[ 33900 = 2^{2} \times 3 \times 5^{2} \times 113 \]33900 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 98952 |
| Euler totient φ(n) | 8960 |
| Square | 1149210000 |
| Cube | 38958219000000 |
| Square root | 184.119526 (= 10√339) |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 111 |
| Scientific notation | 3.39 × |
33900 in other forms
| Form | Value |
|---|---|
| In words | thirty-three thousand nine hundred |
| Binary (base 2) | 1000010001101100 |
| Octal (base 8) | 102154 |
| Hexadecimal (base 16) | 846C |
| Base 3 | 1201111120 |
| As time | 33900 seconds = 9 h 25 min 0 s |
Is 33900 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (33900 ÷ 2 = 16950) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (33900 ÷ 3 = 11300) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (33900 ÷ 4 = 8475) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (33900 ÷ 5 = 6780) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (33900 ÷ 6 = 5650) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 | No (remainder 6) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (33900 ÷ 10 = 3390) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 9) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (33900 ÷ 12 = 2825) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 33900 a prime number?
No. 33900 = × 3 × × 113, so it is divisible by 2.
What are the factors of 33900?
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 113, 150, 226, 300, 339, 452, 565, 678, 1130, 1356, 1695, 2260, 2825, 3390, 5650, 6780, 8475, 11300, 16950, 33900.
What is 33900 in binary?
1000010001101100 (hexadecimal 846C, octal 102154).
What is the square root of 33900?
About 184.1195, exactly 10√339.
Is 33900 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 33900?
33900 is a Harshad number: divisible by its digit sum 15.