The number 30072
30072 is a composite number with 32 divisors. Its prime factorisation is × 3 × 7 × 179. Divisors (32): 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168 … 30072.
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How to work it out
- 1
What is special about 30072: a Harshad number: divisible by its digit sum 12.
- 2
30072 is composite. Its prime factorisation is
- 3
The divisors add up to 86400; without 30072 itself that is 56328, so 30072 is abundant (56328 is more than 30072). Euler's totient φ(30072) = 8544 numbers up to 30072 share no factor with it.
- 4
The digits of 30072 add up to 12, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 90 steps to reach 1.
LaTeX source of the formulas on this page
\[ 30072 = 2^{3} \times 3 \times 7 \times 179 \]30072 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 86400 |
| Euler totient φ(n) | 8544 |
| Square | 904325184 |
| Cube | 27194866933248 |
| Square root | 173.412802 (= 2√7518) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 90 |
| Scientific notation | 3.0072 × |
30072 in other forms
| Form | Value |
|---|---|
| In words | thirty thousand and seventy-two |
| Binary (base 2) | 111010101111000 |
| Octal (base 8) | 72570 |
| Hexadecimal (base 16) | 7578 |
| Base 3 | 1112020210 |
| As time | 30072 seconds = 8 h 21 min 12 s |
Is 30072 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (30072 ÷ 2 = 15036) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (30072 ÷ 3 = 10024) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (30072 ÷ 4 = 7518) | 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 (30072 ÷ 6 = 5012) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (30072 ÷ 7 = 4296) | 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 (30072 ÷ 8 = 3759) | 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 9) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (30072 ÷ 12 = 2506) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 30072 a prime number?
No. 30072 = × 3 × 7 × 179, so it is divisible by 2.
What are the factors of 30072?
1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168, 179, 358, 537, 716, 1074, 1253, 1432, 2148, 2506, 3759, 4296, 5012, 7518, 10024, 15036, 30072.
What is 30072 in binary?
111010101111000 (hexadecimal 7578, octal 72570).
What is the square root of 30072?
About 173.4128, exactly 2√7518.
Is 30072 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 30072?
30072 is a Harshad number: divisible by its digit sum 12.