The number 33670
33670 is a triangular number: 1 + 2 + … + 259 = 33670. Its prime factorisation is 2 × 5 × 7 × 13 × 37. Divisors (32): 1, 2, 5, 7, 10, 13, 14, 26, 35, 37, 65, 70, 74, 91, 130, 182 … 33670.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 33670: a triangular number: 1 + 2 + … + 259 = 33670; a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
33670 is composite. Its prime factorisation is
- 3
The divisors add up to 76608; without 33670 itself that is 42938, so 33670 is abundant (42938 is more than 33670). Euler's totient φ(33670) = 10368 numbers up to 33670 share no factor with it.
- 4
The digits of 33670 add up to 19, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 160 steps to reach 1.
LaTeX source of the formulas on this page
\[ 33670 = 2 \times 5 \times 7 \times 13 \times 37 \]
33670 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 76608 |
| Euler totient φ(n) | 10368 |
| Square | 1133668900 |
| Cube | 38170631863000 |
| Square root | 183.493869 |
| Digit sum / digital root | 19 / 1 |
| Collatz steps to 1 | 160 |
| Scientific notation | 3.367 × |
33670 in other forms
| Form | Value |
|---|---|
| In words | thirty-three thousand six hundred and seventy |
| Binary (base 2) | 1000001110000110 |
| Octal (base 8) | 101606 |
| Hexadecimal (base 16) | 8386 |
| Base 3 | 1201012001 |
| As time | 33670 seconds = 9 h 21 min 10 s |
Is 33670 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (33670 ÷ 2 = 16835) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 2) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (33670 ÷ 5 = 6734) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 4) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (33670 ÷ 7 = 4810) | 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 6) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 1) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (33670 ÷ 10 = 3367) | 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 | No (remainder 10) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 33670 a prime number?
No. 33670 = 2 × 5 × 7 × 13 × 37, so it is divisible by 2.
What are the factors of 33670?
1, 2, 5, 7, 10, 13, 14, 26, 35, 37, 65, 70, 74, 91, 130, 182, 185, 259, 370, 455, 481, 518, 910, 962, 1295, 2405, 2590, 3367, 4810, 6734, 16835, 33670.
What is 33670 in binary?
1000001110000110 (hexadecimal 8386, octal 101606).
What is the square root of 33670?
About 183.4939.
Is 33670 divisible by 3?
No. Its digits add up to 19, which is not a multiple of 3.
What is special about the number 33670?
33670 is a triangular number: 1 + 2 + … + 259 = 33670; a happy number: repeatedly adding the squares of its digits reaches 1.