The number 21180
21180 is a composite number with 24 divisors. Its prime factorisation is × 3 × 5 × 353. Divisors (24): 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 353, 706, 1059, 1412 … 21180.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 21180: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 12.
- 2
21180 is composite. Its prime factorisation is
- 3
The divisors add up to 59472; without 21180 itself that is 38292, so 21180 is abundant (38292 is more than 21180). Euler's totient φ(21180) = 5632 numbers up to 21180 share no factor with it.
- 4
The digits of 21180 add up to 12, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 149 steps to reach 1.
LaTeX source of the formulas on this page
\[ 21180 = 2^{2} \times 3 \times 5 \times 353 \]21180 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 59472 |
| Euler totient φ(n) | 5632 |
| Square | 448592400 |
| Cube | 9501187032000 |
| Square root | 145.533501 (= 2√5295) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 149 |
| Scientific notation | 2.118 × |
21180 in other forms
| Form | Value |
|---|---|
| In words | twenty-one thousand one hundred and eighty |
| Binary (base 2) | 101001010111100 |
| Octal (base 8) | 51274 |
| Hexadecimal (base 16) | 52BC |
| Base 3 | 1002001110 |
| As time | 21180 seconds = 5 h 53 min 0 s |
Is 21180 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (21180 ÷ 2 = 10590) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (21180 ÷ 3 = 7060) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (21180 ÷ 4 = 5295) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (21180 ÷ 5 = 4236) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (21180 ÷ 6 = 3530) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 | No (remainder 3) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (21180 ÷ 10 = 2118) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 5) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (21180 ÷ 12 = 1765) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 21180 a prime number?
No. 21180 = × 3 × 5 × 353, so it is divisible by 2.
What are the factors of 21180?
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 353, 706, 1059, 1412, 1765, 2118, 3530, 4236, 5295, 7060, 10590, 21180.
What is 21180 in binary?
101001010111100 (hexadecimal 52BC, octal 51274).
What is the square root of 21180?
About 145.5335, exactly 2√5295.
Is 21180 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 21180?
21180 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 12.