The number 21120
21120 is a composite number with 64 divisors. Its prime factorisation is × 3 × 5 × 11. Divisors (64): 1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 16, 20, 22, 24, 30 … 21120.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 21120: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 6.
- 2
21120 is composite. Its prime factorisation is
- 3
The divisors add up to 73440; without 21120 itself that is 52320, so 21120 is abundant (52320 is more than 21120). Euler's totient φ(21120) = 5120 numbers up to 21120 share no factor with it.
- 4
The digits of 21120 add up to 6, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 118 steps to reach 1.
LaTeX source of the formulas on this page
\[ 21120 = 2^{7} \times 3 \times 5 \times 11 \]21120 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 64 |
| Sum of divisors | 73440 |
| Euler totient φ(n) | 5120 |
| Square | 446054400 |
| Cube | 9420668928000 |
| Square root | 145.327217 (= 8√330) |
| Digit sum / digital root | 6 / 6 |
| Collatz steps to 1 | 118 |
| Scientific notation | 2.112 × |
21120 in other forms
| Form | Value |
|---|---|
| In words | twenty-one thousand one hundred and twenty |
| Binary (base 2) | 101001010000000 |
| Octal (base 8) | 51200 |
| Hexadecimal (base 16) | 5280 |
| Base 3 | 1001222020 |
| As time | 21120 seconds = 5 h 52 min 0 s |
Is 21120 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (21120 ÷ 2 = 10560) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (21120 ÷ 3 = 7040) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (21120 ÷ 4 = 5280) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (21120 ÷ 5 = 4224) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (21120 ÷ 6 = 3520) | 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 (21120 ÷ 8 = 2640) | 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 (21120 ÷ 10 = 2112) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (21120 ÷ 11 = 1920) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (21120 ÷ 12 = 1760) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 21120 a prime number?
No. 21120 = × 3 × 5 × 11, so it is divisible by 2.
What are the factors of 21120?
1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 16, 20, 22, 24, 30, 32, 33, 40, 44, 48, 55, 60, 64, 66, 80, 88, 96, 110, 120, 128, 132, 160, 165, 176, 192, 220, 240, 264, 320, 330, 352, 384, 440, 480, 528, 640, 660, 704, 880, 960, 1056, 1320, 1408, 1760, 1920, 2112, 2640, 3520, 4224, 5280, 7040, 10560, 21120.
What is 21120 in binary?
101001010000000 (hexadecimal 5280, octal 51200).
What is the square root of 21120?
About 145.3272, exactly 8√330.
Is 21120 divisible by 3?
Yes. Its digits add up to 6, a multiple of 3.
What is special about the number 21120?
21120 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 6.