The number 39120
39120 is a composite number with 40 divisors. Its prime factorisation is × 3 × 5 × 163. Divisors (40): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48 … 39120.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 39120: a Harshad number: divisible by its digit sum 15.
- 2
39120 is composite. Its prime factorisation is
- 3
The divisors add up to 122016; without 39120 itself that is 82896, so 39120 is abundant (82896 is more than 39120). Euler's totient φ(39120) = 10368 numbers up to 39120 share no factor with it.
- 4
The digits of 39120 add up to 15, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 44 steps to reach 1.
LaTeX source of the formulas on this page
\[ 39120 = 2^{4} \times 3 \times 5 \times 163 \]39120 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 40 |
| Sum of divisors | 122016 |
| Euler totient φ(n) | 10368 |
| Square | 1530374400 |
| Cube | 59868246528000 |
| Square root | 197.787765 (= 4√2445) |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 44 |
| Scientific notation | 3.912 × |
39120 in other forms
| Form | Value |
|---|---|
| In words | thirty-nine thousand one hundred and twenty |
| Binary (base 2) | 1001100011010000 |
| Octal (base 8) | 114320 |
| Hexadecimal (base 16) | 98D0 |
| Base 3 | 1222122220 |
| As time | 39120 seconds = 10 h 52 min 0 s |
Is 39120 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (39120 ÷ 2 = 19560) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (39120 ÷ 3 = 13040) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (39120 ÷ 4 = 9780) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (39120 ÷ 5 = 7824) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (39120 ÷ 6 = 6520) | 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 | Yes (39120 ÷ 8 = 4890) | 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 | Yes (39120 ÷ 10 = 3912) | 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 (39120 ÷ 12 = 3260) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 39120 a prime number?
No. 39120 = × 3 × 5 × 163, so it is divisible by 2.
What are the factors of 39120?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 163, 240, 326, 489, 652, 815, 978, 1304, 1630, 1956, 2445, 2608, 3260, 3912, 4890, 6520, 7824, 9780, 13040, 19560, 39120.
What is 39120 in binary?
1001100011010000 (hexadecimal 98D0, octal 114320).
What is the square root of 39120?
About 197.7878, exactly 4√2445.
Is 39120 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 39120?
39120 is a Harshad number: divisible by its digit sum 15.