The number 1582
1582 is a composite number with 8 divisors. Its prime factorisation is 2 × 7 × 113. Divisors (8): 1, 2, 7, 14, 113, 226, 791, 1582.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1582: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
1582 is composite. Its prime factorisation is
- 3
The divisors add up to 2736; without 1582 itself that is 1154, so 1582 is deficient (1154 is less than 1582). Euler's totient φ(1582) = 672 numbers up to 1582 share no factor with it.
- 4
The digits of 1582 add up to 16, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 78 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1582 = 2 \times 7 \times 113 \]
1582 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 8 |
| Sum of divisors | 2736 |
| Euler totient φ(n) | 672 |
| Square | 2502724 |
| Cube | 3959309368 |
| Square root | 39.774364 |
| Digit sum / digital root | 16 / 7 |
| Collatz steps to 1 | 78 |
| Scientific notation | 1.582 × |
1582 in other forms
| Form | Value |
|---|---|
| In words | one thousand five hundred and eighty-two |
| Roman numerals | MDLXXXII |
| Binary (base 2) | 11000101110 |
| Octal (base 8) | 3056 |
| Hexadecimal (base 16) | 62E |
| Base 3 | 2011121 |
| As time | 1582 seconds = 26 min 22 s |
Is 1582 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (1582 ÷ 2 = 791) | 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 | No (remainder 2) | 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 | Yes (1582 ÷ 7 = 226) | 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 6) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 7) | 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 | No (remainder 10) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1582 a prime number?
No. 1582 = 2 × 7 × 113, so it is divisible by 2.
What are the factors of 1582?
1, 2, 7, 14, 113, 226, 791, 1582.
What is 1582 in binary?
11000101110 (hexadecimal 62E, octal 3056).
What is the square root of 1582?
About 39.7744.
What is 1582 in Roman numerals?
MDLXXXII.
Is 1582 divisible by 3?
No. Its digits add up to 16, which is not a multiple of 3.
What is special about the number 1582?
1582 is a happy number: repeatedly adding the squares of its digits reaches 1.