The number 29970
29970 is a composite number with 40 divisors. Its prime factorisation is 2 × × 5 × 37. Divisors (40): 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 37, 45, 54, 74, 81 … 29970.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 29970: a Harshad number: divisible by its digit sum 27.
- 2
29970 is composite. Its prime factorisation is
- 3
The divisors add up to 82764; without 29970 itself that is 52794, so 29970 is abundant (52794 is more than 29970). Euler's totient φ(29970) = 7776 numbers up to 29970 share no factor with it.
- 4
The digits of 29970 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 64 steps to reach 1.
LaTeX source of the formulas on this page
\[ 29970 = 2 \times 3^{4} \times 5 \times 37 \]29970 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 40 |
| Sum of divisors | 82764 |
| Euler totient φ(n) | 7776 |
| Square | 898200900 |
| Cube | 26919080973000 |
| Square root | 173.118457 (= 9√370) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 64 |
| Scientific notation | 2.997 × |
29970 in other forms
| Form | Value |
|---|---|
| In words | twenty-nine thousand nine hundred and seventy |
| Binary (base 2) | 111010100010010 |
| Octal (base 8) | 72422 |
| Hexadecimal (base 16) | 7512 |
| Base 3 | 1112010000 |
| As time | 29970 seconds = 8 h 19 min 30 s |
Is 29970 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (29970 ÷ 2 = 14985) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (29970 ÷ 3 = 9990) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 2) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (29970 ÷ 5 = 5994) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (29970 ÷ 6 = 4995) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 2) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (29970 ÷ 9 = 3330) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (29970 ÷ 10 = 2997) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 6) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 29970 a prime number?
No. 29970 = 2 × × 5 × 37, so it is divisible by 2.
What are the factors of 29970?
1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 37, 45, 54, 74, 81, 90, 111, 135, 162, 185, 222, 270, 333, 370, 405, 555, 666, 810, 999, 1110, 1665, 1998, 2997, 3330, 4995, 5994, 9990, 14985, 29970.
What is 29970 in binary?
111010100010010 (hexadecimal 7512, octal 72422).
What is the square root of 29970?
About 173.1185, exactly 9√370.
Is 29970 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 29970?
29970 is a Harshad number: divisible by its digit sum 27.