The number 10072
10072 is a composite number with 8 divisors. Its prime factorisation is × 1259. Divisors (8): 1, 2, 4, 8, 1259, 2518, 5036, 10072.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
10072 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
10072 is composite. Its prime factorisation is
- 3
The divisors add up to 18900; without 10072 itself that is 8828, so 10072 is deficient (8828 is less than 10072). Euler's totient φ(10072) = 5032 numbers up to 10072 share no factor with it.
- 4
The digits of 10072 add up to 10, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 86 steps to reach 1.
LaTeX source of the formulas on this page
\[ 10072 = 2^{3} \times 1259 \]10072 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 8 |
| Sum of divisors | 18900 |
| Euler totient φ(n) | 5032 |
| Square | 101445184 |
| Cube | 1021755893248 |
| Square root | 100.359354 (= 2√2518) |
| Digit sum / digital root | 10 / 1 |
| Collatz steps to 1 | 86 |
| Scientific notation | 1.0072 × |
10072 in other forms
| Form | Value |
|---|---|
| In words | ten thousand and seventy-two |
| Binary (base 2) | 10011101011000 |
| Octal (base 8) | 23530 |
| Hexadecimal (base 16) | 2758 |
| Base 3 | 111211001 |
| As time | 10072 seconds = 2 h 47 min 52 s |
Is 10072 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (10072 ÷ 2 = 5036) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (10072 ÷ 4 = 2518) | 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 | No (remainder 4) | 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 | Yes (10072 ÷ 8 = 1259) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 1) | 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 7) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 10072 a prime number?
No. 10072 = × 1259, so it is divisible by 2.
What are the factors of 10072?
1, 2, 4, 8, 1259, 2518, 5036, 10072.
What is 10072 in binary?
10011101011000 (hexadecimal 2758, octal 23530).
What is the square root of 10072?
About 100.3594, exactly 2√2518.
Is 10072 divisible by 3?
No. Its digits add up to 10, which is not a multiple of 3.
What is special about the number 10072?
It is a composite number with 8 divisors.