The number 33972
33972 is a composite number with 24 divisors. Its prime factorisation is × 3 × 19 × 149. Divisors (24): 1, 2, 3, 4, 6, 12, 19, 38, 57, 76, 114, 149, 228, 298, 447, 596 … 33972.
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How to work it out
- 1
33972 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
33972 is composite. Its prime factorisation is
- 3
The divisors add up to 84000; without 33972 itself that is 50028, so 33972 is abundant (50028 is more than 33972). Euler's totient φ(33972) = 10656 numbers up to 33972 share no factor with it.
- 4
The digits of 33972 add up to 24, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 36 steps to reach 1.
LaTeX source of the formulas on this page
\[ 33972 = 2^{2} \times 3 \times 19 \times 149 \]33972 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 84000 |
| Euler totient φ(n) | 10656 |
| Square | 1154096784 |
| Cube | 39206975946048 |
| Square root | 184.314948 (= 2√8493) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 36 |
| Scientific notation | 3.3972 × |
33972 in other forms
| Form | Value |
|---|---|
| In words | thirty-three thousand nine hundred and seventy-two |
| Binary (base 2) | 1000010010110100 |
| Octal (base 8) | 102264 |
| Hexadecimal (base 16) | 84B4 |
| Base 3 | 1201121020 |
| As time | 33972 seconds = 9 h 26 min 12 s |
Is 33972 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (33972 ÷ 2 = 16986) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (33972 ÷ 3 = 11324) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (33972 ÷ 4 = 8493) | 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 | Yes (33972 ÷ 6 = 5662) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 1) | 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 | No (remainder 2) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (33972 ÷ 12 = 2831) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 33972 a prime number?
No. 33972 = × 3 × 19 × 149, so it is divisible by 2.
What are the factors of 33972?
1, 2, 3, 4, 6, 12, 19, 38, 57, 76, 114, 149, 228, 298, 447, 596, 894, 1788, 2831, 5662, 8493, 11324, 16986, 33972.
What is 33972 in binary?
1000010010110100 (hexadecimal 84B4, octal 102264).
What is the square root of 33972?
About 184.3149, exactly 2√8493.
Is 33972 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 33972?
It is a composite number with 24 divisors.