The number 21132
21132 is a composite number with 18 divisors. Its prime factorisation is × × 587. Divisors (18): 1, 2, 3, 4, 6, 9, 12, 18, 36, 587, 1174, 1761, 2348, 3522, 5283, 7044 … 21132.
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How to work it out
- 1
What is special about 21132: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 9.
- 2
21132 is composite. Its prime factorisation is
- 3
The divisors add up to 53508; without 21132 itself that is 32376, so 21132 is abundant (32376 is more than 21132). Euler's totient φ(21132) = 7032 numbers up to 21132 share no factor with it.
- 4
The digits of 21132 add up to 9, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 105 steps to reach 1.
LaTeX source of the formulas on this page
\[ 21132 = 2^{2} \times 3^{2} \times 587 \]21132 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 18 |
| Sum of divisors | 53508 |
| Euler totient φ(n) | 7032 |
| Square | 446561424 |
| Cube | 9436736011968 |
| Square root | 145.368497 (= 6√587) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 105 |
| Scientific notation | 2.1132 × |
21132 in other forms
| Form | Value |
|---|---|
| In words | twenty-one thousand one hundred and thirty-two |
| Binary (base 2) | 101001010001100 |
| Octal (base 8) | 51214 |
| Hexadecimal (base 16) | 528C |
| Base 3 | 1001222200 |
| As time | 21132 seconds = 5 h 52 min 12 s |
Is 21132 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (21132 ÷ 2 = 10566) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (21132 ÷ 3 = 7044) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (21132 ÷ 4 = 5283) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 2) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (21132 ÷ 6 = 3522) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (21132 ÷ 9 = 2348) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 2) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (21132 ÷ 12 = 1761) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 21132 a prime number?
No. 21132 = × × 587, so it is divisible by 2.
What are the factors of 21132?
1, 2, 3, 4, 6, 9, 12, 18, 36, 587, 1174, 1761, 2348, 3522, 5283, 7044, 10566, 21132.
What is 21132 in binary?
101001010001100 (hexadecimal 528C, octal 51214).
What is the square root of 21132?
About 145.3685, exactly 6√587.
Is 21132 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 21132?
21132 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 9.