The number 33768
33768 is a composite number with 48 divisors. Its prime factorisation is × × 7 × 67. Divisors (48): 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42 … 33768.
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How to work it out
- 1
What is special about 33768: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
33768 is composite. Its prime factorisation is
- 3
The divisors add up to 106080; without 33768 itself that is 72312, so 33768 is abundant (72312 is more than 33768). Euler's totient φ(33768) = 9504 numbers up to 33768 share no factor with it.
- 4
The digits of 33768 add up to 27, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 173 steps to reach 1.
LaTeX source of the formulas on this page
\[ 33768 = 2^{3} \times 3^{2} \times 7 \times 67 \]33768 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 106080 |
| Euler totient φ(n) | 9504 |
| Square | 1140277824 |
| Cube | 38504901560832 |
| Square root | 183.760714 (= 6√938) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 173 |
| Scientific notation | 3.3768 × |
33768 in other forms
| Form | Value |
|---|---|
| In words | thirty-three thousand seven hundred and sixty-eight |
| Binary (base 2) | 1000001111101000 |
| Octal (base 8) | 101750 |
| Hexadecimal (base 16) | 83E8 |
| Base 3 | 1201022200 |
| As time | 33768 seconds = 9 h 22 min 48 s |
Is 33768 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (33768 ÷ 2 = 16884) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (33768 ÷ 3 = 11256) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (33768 ÷ 4 = 8442) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 3) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (33768 ÷ 6 = 5628) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (33768 ÷ 7 = 4824) | 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 (33768 ÷ 8 = 4221) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (33768 ÷ 9 = 3752) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 8) | 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 (33768 ÷ 12 = 2814) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 33768 a prime number?
No. 33768 = × × 7 × 67, so it is divisible by 2.
What are the factors of 33768?
1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 56, 63, 67, 72, 84, 126, 134, 168, 201, 252, 268, 402, 469, 504, 536, 603, 804, 938, 1206, 1407, 1608, 1876, 2412, 2814, 3752, 4221, 4824, 5628, 8442, 11256, 16884, 33768.
What is 33768 in binary?
1000001111101000 (hexadecimal 83E8, octal 101750).
What is the square root of 33768?
About 183.7607, exactly 6√938.
Is 33768 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 33768?
33768 is a happy number: repeatedly adding the squares of its digits reaches 1.