The number 33872
33872 is a composite number with 20 divisors. Its prime factorisation is × 29 × 73. Divisors (20): 1, 2, 4, 8, 16, 29, 58, 73, 116, 146, 232, 292, 464, 584, 1168, 2117 … 33872.
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How to work it out
- 1
33872 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
33872 is composite. Its prime factorisation is
- 3
The divisors add up to 68820; without 33872 itself that is 34948, so 33872 is abundant (34948 is more than 33872). Euler's totient φ(33872) = 16128 numbers up to 33872 share no factor with it.
- 4
The digits of 33872 add up to 23, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 36 steps to reach 1.
LaTeX source of the formulas on this page
\[ 33872 = 2^{4} \times 29 \times 73 \]33872 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 20 |
| Sum of divisors | 68820 |
| Euler totient φ(n) | 16128 |
| Square | 1147312384 |
| Cube | 38861765070848 |
| Square root | 184.043473 (= 4√2117) |
| Digit sum / digital root | 23 / 5 |
| Collatz steps to 1 | 36 |
| Scientific notation | 3.3872 × |
33872 in other forms
| Form | Value |
|---|---|
| In words | thirty-three thousand eight hundred and seventy-two |
| Binary (base 2) | 1000010001010000 |
| Octal (base 8) | 102120 |
| Hexadecimal (base 16) | 8450 |
| Base 3 | 1201110112 |
| As time | 33872 seconds = 9 h 24 min 32 s |
Is 33872 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (33872 ÷ 2 = 16936) | 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 (33872 ÷ 4 = 8468) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 2) | 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 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 | Yes (33872 ÷ 8 = 4234) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 5) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 2) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 3) | 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 33872 a prime number?
No. 33872 = × 29 × 73, so it is divisible by 2.
What are the factors of 33872?
1, 2, 4, 8, 16, 29, 58, 73, 116, 146, 232, 292, 464, 584, 1168, 2117, 4234, 8468, 16936, 33872.
What is 33872 in binary?
1000010001010000 (hexadecimal 8450, octal 102120).
What is the square root of 33872?
About 184.0435, exactly 4√2117.
Is 33872 divisible by 3?
No. Its digits add up to 23, which is not a multiple of 3.
What is special about the number 33872?
It is a composite number with 20 divisors.