The number 36960
36960 is a composite number with 96 divisors. Its prime factorisation is × 3 × 5 × 7 × 11. Divisors (96): 1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 14, 15, 16, 20, 21 … 36960.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 36960: a Harshad number: divisible by its digit sum 24.
- 2
36960 is composite. Its prime factorisation is
- 3
The divisors add up to 145152; without 36960 itself that is 108192, so 36960 is abundant (108192 is more than 36960). Euler's totient φ(36960) = 7680 numbers up to 36960 share no factor with it.
- 4
The digits of 36960 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
\[ 36960 = 2^{5} \times 3 \times 5 \times 7 \times 11 \]36960 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 96 |
| Sum of divisors | 145152 |
| Euler totient φ(n) | 7680 |
| Square | 1366041600 |
| Cube | 50488897536000 |
| Square root | 192.249837 (= 4√2310) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 36 |
| Scientific notation | 3.696 × |
36960 in other forms
| Form | Value |
|---|---|
| In words | thirty-six thousand nine hundred and sixty |
| Binary (base 2) | 1001000001100000 |
| Octal (base 8) | 110140 |
| Hexadecimal (base 16) | 9060 |
| Base 3 | 1212200220 |
| As time | 36960 seconds = 10 h 16 min 0 s |
Is 36960 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (36960 ÷ 2 = 18480) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (36960 ÷ 3 = 12320) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (36960 ÷ 4 = 9240) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (36960 ÷ 5 = 7392) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (36960 ÷ 6 = 6160) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (36960 ÷ 7 = 5280) | 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 (36960 ÷ 8 = 4620) | 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 (36960 ÷ 10 = 3696) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (36960 ÷ 11 = 3360) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (36960 ÷ 12 = 3080) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 36960 a prime number?
No. 36960 = × 3 × 5 × 7 × 11, so it is divisible by 2.
What are the factors of 36960?
1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 14, 15, 16, 20, 21, 22, 24, 28, 30, 32, 33, 35, 40, 42, 44, 48, 55, 56, 60, 66, 70, 77, 80, 84, 88, 96, 105, 110, 112, 120, 132, 140, 154, 160, 165, 168, 176, 210, 220, 224, 231, 240, 264, 280, 308, 330, 336, 352, 385, 420, 440, 462, 480, 528, 560, 616, 660, 672, 770, 840, 880, 924, 1056, 1120, 1155, 1232, 1320, 1540, 1680, 1760, 1848, 2310, 2464, 2640, 3080, 3360, 3696, 4620, 5280, 6160, 7392, 9240, 12320, 18480, 36960.
What is 36960 in binary?
1001000001100000 (hexadecimal 9060, octal 110140).
What is the square root of 36960?
About 192.2498, exactly 4√2310.
Is 36960 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 36960?
36960 is a Harshad number: divisible by its digit sum 24.