The number 10212
10212 is a composite number with 24 divisors. Its prime factorisation is × 3 × 23 × 37. Divisors (24): 1, 2, 3, 4, 6, 12, 23, 37, 46, 69, 74, 92, 111, 138, 148, 222 … 10212.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 10212: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 6.
- 2
10212 is composite. Its prime factorisation is
- 3
The divisors add up to 25536; without 10212 itself that is 15324, so 10212 is abundant (15324 is more than 10212). Euler's totient φ(10212) = 3168 numbers up to 10212 share no factor with it.
- 4
The digits of 10212 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 179 steps to reach 1.
LaTeX source of the formulas on this page
\[ 10212 = 2^{2} \times 3 \times 23 \times 37 \]10212 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 25536 |
| Euler totient φ(n) | 3168 |
| Square | 104284944 |
| Cube | 1064957848128 |
| Square root | 101.054441 (= 2√2553) |
| Digit sum / digital root | 6 / 6 |
| Collatz steps to 1 | 179 |
| Scientific notation | 1.0212 × |
10212 in other forms
| Form | Value |
|---|---|
| In words | ten thousand two hundred and twelve |
| Binary (base 2) | 10011111100100 |
| Octal (base 8) | 23744 |
| Hexadecimal (base 16) | 27E4 |
| Base 3 | 112000020 |
| As time | 10212 seconds = 2 h 50 min 12 s |
Is 10212 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (10212 ÷ 2 = 5106) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (10212 ÷ 3 = 3404) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (10212 ÷ 4 = 2553) | 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 (10212 ÷ 6 = 1702) | 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 6) | 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 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (10212 ÷ 12 = 851) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 10212 a prime number?
No. 10212 = × 3 × 23 × 37, so it is divisible by 2.
What are the factors of 10212?
1, 2, 3, 4, 6, 12, 23, 37, 46, 69, 74, 92, 111, 138, 148, 222, 276, 444, 851, 1702, 2553, 3404, 5106, 10212.
What is 10212 in binary?
10011111100100 (hexadecimal 27E4, octal 23744).
What is the square root of 10212?
About 101.0544, exactly 2√2553.
Is 10212 divisible by 3?
Yes. Its digits add up to 6, a multiple of 3.
What is special about the number 10212?
10212 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 6.