The number 1072
1072 is a composite number with 10 divisors. Its prime factorisation is × 67. Divisors (10): 1, 2, 4, 8, 16, 67, 134, 268, 536, 1072.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
1072 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
1072 is composite. Its prime factorisation is
- 3
The divisors add up to 2108; without 1072 itself that is 1036, so 1072 is deficient (1036 is less than 1072). Euler's totient φ(1072) = 528 numbers up to 1072 share no factor with it.
- 4
The digits of 1072 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 31 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1072 = 2^{4} \times 67 \]1072 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 10 |
| Sum of divisors | 2108 |
| Euler totient φ(n) | 528 |
| Square | 1149184 |
| Cube | 1231925248 |
| Square root | 32.741411 (= 4√67) |
| Digit sum / digital root | 10 / 1 |
| Collatz steps to 1 | 31 |
| Scientific notation | 1.072 × |
1072 in other forms
| Form | Value |
|---|---|
| In words | one thousand and seventy-two |
| Roman numerals | MLXXII |
| Binary (base 2) | 10000110000 |
| Octal (base 8) | 2060 |
| Hexadecimal (base 16) | 430 |
| Base 3 | 1110201 |
| As time | 1072 seconds = 17 min 52 s |
Is 1072 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (1072 ÷ 2 = 536) | 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 (1072 ÷ 4 = 268) | 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 1) | 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 (1072 ÷ 8 = 134) | 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 5) | 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 1072 a prime number?
No. 1072 = × 67, so it is divisible by 2.
What are the factors of 1072?
1, 2, 4, 8, 16, 67, 134, 268, 536, 1072.
What is 1072 in binary?
10000110000 (hexadecimal 430, octal 2060).
What is the square root of 1072?
About 32.7414, exactly 4√67.
What is 1072 in Roman numerals?
MLXXII.
Is 1072 divisible by 3?
No. Its digits add up to 10, which is not a multiple of 3.
What is special about the number 1072?
It is a composite number with 10 divisors.