The number 10272
10272 is a composite number with 24 divisors. Its prime factorisation is × 3 × 107. Divisors (24): 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 107, 214, 321, 428 … 10272.
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How to work it out
- 1
What is special about 10272: a Harshad number: divisible by its digit sum 12.
- 2
10272 is composite. Its prime factorisation is
- 3
The divisors add up to 27216; without 10272 itself that is 16944, so 10272 is abundant (16944 is more than 10272). Euler's totient φ(10272) = 3392 numbers up to 10272 share no factor with it.
- 4
The digits of 10272 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 29 steps to reach 1.
LaTeX source of the formulas on this page
\[ 10272 = 2^{5} \times 3 \times 107 \]10272 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 27216 |
| Euler totient φ(n) | 3392 |
| Square | 105513984 |
| Cube | 1083839643648 |
| Square root | 101.350876 (= 4√642) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 29 |
| Scientific notation | 1.0272 × |
10272 in other forms
| Form | Value |
|---|---|
| In words | ten thousand two hundred and seventy-two |
| Binary (base 2) | 10100000100000 |
| Octal (base 8) | 24040 |
| Hexadecimal (base 16) | 2820 |
| Base 3 | 112002110 |
| As time | 10272 seconds = 2 h 51 min 12 s |
Is 10272 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (10272 ÷ 2 = 5136) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (10272 ÷ 3 = 3424) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (10272 ÷ 4 = 2568) | 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 (10272 ÷ 6 = 1712) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 (10272 ÷ 8 = 1284) | 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 | No (remainder 2) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 9) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (10272 ÷ 12 = 856) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 10272 a prime number?
No. 10272 = × 3 × 107, so it is divisible by 2.
What are the factors of 10272?
1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 107, 214, 321, 428, 642, 856, 1284, 1712, 2568, 3424, 5136, 10272.
What is 10272 in binary?
10100000100000 (hexadecimal 2820, octal 24040).
What is the square root of 10272?
About 101.3509, exactly 4√642.
Is 10272 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 10272?
10272 is a Harshad number: divisible by its digit sum 12.