The number 30972
30972 is a composite number with 24 divisors. Its prime factorisation is × 3 × 29 × 89. Divisors (24): 1, 2, 3, 4, 6, 12, 29, 58, 87, 89, 116, 174, 178, 267, 348, 356 … 30972.
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How to work it out
- 1
30972 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
30972 is composite. Its prime factorisation is
- 3
The divisors add up to 75600; without 30972 itself that is 44628, so 30972 is abundant (44628 is more than 30972). Euler's totient φ(30972) = 9856 numbers up to 30972 share no factor with it.
- 4
The digits of 30972 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 116 steps to reach 1.
LaTeX source of the formulas on this page
\[ 30972 = 2^{2} \times 3 \times 29 \times 89 \]30972 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 75600 |
| Euler totient φ(n) | 9856 |
| Square | 959264784 |
| Cube | 29710348890048 |
| Square root | 175.988636 (= 2√7743) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 116 |
| Scientific notation | 3.0972 × |
30972 in other forms
| Form | Value |
|---|---|
| In words | thirty thousand nine hundred and seventy-two |
| Binary (base 2) | 111100011111100 |
| Octal (base 8) | 74374 |
| Hexadecimal (base 16) | 78FC |
| Base 3 | 1120111010 |
| As time | 30972 seconds = 8 h 36 min 12 s |
Is 30972 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (30972 ÷ 2 = 15486) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (30972 ÷ 3 = 10324) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (30972 ÷ 4 = 7743) | 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 (30972 ÷ 6 = 5162) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 3) | 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 7) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (30972 ÷ 12 = 2581) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 30972 a prime number?
No. 30972 = × 3 × 29 × 89, so it is divisible by 2.
What are the factors of 30972?
1, 2, 3, 4, 6, 12, 29, 58, 87, 89, 116, 174, 178, 267, 348, 356, 534, 1068, 2581, 5162, 7743, 10324, 15486, 30972.
What is 30972 in binary?
111100011111100 (hexadecimal 78FC, octal 74374).
What is the square root of 30972?
About 175.9886, exactly 2√7743.
Is 30972 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 30972?
It is a composite number with 24 divisors.