The number 12900
12900 is a composite number with 36 divisors. Its prime factorisation is × 3 × × 43. Divisors (36): 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 43, 50, 60, 75 … 12900.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 12900: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 12.
- 2
12900 is composite. Its prime factorisation is
- 3
The divisors add up to 38192; without 12900 itself that is 25292, so 12900 is abundant (25292 is more than 12900). Euler's totient φ(12900) = 3360 numbers up to 12900 share no factor with it.
- 4
The digits of 12900 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 63 steps to reach 1.
LaTeX source of the formulas on this page
\[ 12900 = 2^{2} \times 3 \times 5^{2} \times 43 \]12900 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 38192 |
| Euler totient φ(n) | 3360 |
| Square | 166410000 |
| Cube | 2146689000000 |
| Square root | 113.578167 (= 10√129) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 63 |
| Scientific notation | 1.29 × |
12900 in other forms
| Form | Value |
|---|---|
| In words | twelve thousand nine hundred |
| Binary (base 2) | 11001001100100 |
| Octal (base 8) | 31144 |
| Hexadecimal (base 16) | 3264 |
| Base 3 | 122200210 |
| As time | 12900 seconds = 3 h 35 min 0 s |
Is 12900 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (12900 ÷ 2 = 6450) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (12900 ÷ 3 = 4300) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (12900 ÷ 4 = 3225) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (12900 ÷ 5 = 2580) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (12900 ÷ 6 = 2150) | 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 | No (remainder 3) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (12900 ÷ 10 = 1290) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 8) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (12900 ÷ 12 = 1075) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 12900 a prime number?
No. 12900 = × 3 × × 43, so it is divisible by 2.
What are the factors of 12900?
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 43, 50, 60, 75, 86, 100, 129, 150, 172, 215, 258, 300, 430, 516, 645, 860, 1075, 1290, 2150, 2580, 3225, 4300, 6450, 12900.
What is 12900 in binary?
11001001100100 (hexadecimal 3264, octal 31144).
What is the square root of 12900?
About 113.5782, exactly 10√129.
Is 12900 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 12900?
12900 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 12.