The number 21960
21960 is a composite number with 48 divisors. Its prime factorisation is × × 5 × 61. Divisors (48): 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36 … 21960.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 21960: a Harshad number: divisible by its digit sum 18.
- 2
21960 is composite. Its prime factorisation is
- 3
The divisors add up to 72540; without 21960 itself that is 50580, so 21960 is abundant (50580 is more than 21960). Euler's totient φ(21960) = 5760 numbers up to 21960 share no factor with it.
- 4
The digits of 21960 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 43 steps to reach 1.
LaTeX source of the formulas on this page
\[ 21960 = 2^{3} \times 3^{2} \times 5 \times 61 \]21960 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 72540 |
| Euler totient φ(n) | 5760 |
| Square | 482241600 |
| Cube | 10590025536000 |
| Square root | 148.189068 (= 6√610) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 43 |
| Scientific notation | 2.196 × |
21960 in other forms
| Form | Value |
|---|---|
| In words | twenty-one thousand nine hundred and sixty |
| Binary (base 2) | 101010111001000 |
| Octal (base 8) | 52710 |
| Hexadecimal (base 16) | 55C8 |
| Base 3 | 1010010100 |
| As time | 21960 seconds = 6 h 6 min 0 s |
Is 21960 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (21960 ÷ 2 = 10980) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (21960 ÷ 3 = 7320) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (21960 ÷ 4 = 5490) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (21960 ÷ 5 = 4392) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (21960 ÷ 6 = 3660) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 1) | 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 (21960 ÷ 8 = 2745) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (21960 ÷ 9 = 2440) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (21960 ÷ 10 = 2196) | 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 (21960 ÷ 12 = 1830) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 21960 a prime number?
No. 21960 = × × 5 × 61, so it is divisible by 2.
What are the factors of 21960?
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 61, 72, 90, 120, 122, 180, 183, 244, 305, 360, 366, 488, 549, 610, 732, 915, 1098, 1220, 1464, 1830, 2196, 2440, 2745, 3660, 4392, 5490, 7320, 10980, 21960.
What is 21960 in binary?
101010111001000 (hexadecimal 55C8, octal 52710).
What is the square root of 21960?
About 148.1891, exactly 6√610.
Is 21960 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 21960?
21960 is a Harshad number: divisible by its digit sum 18.