The number 1580
1580 is a composite number with 12 divisors. Its prime factorisation is × 5 × 79. Divisors (12): 1, 2, 4, 5, 10, 20, 79, 158, 316, 395, 790, 1580.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
1580 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
1580 is composite. Its prime factorisation is
- 3
The divisors add up to 3360; without 1580 itself that is 1780, so 1580 is abundant (1780 is more than 1580). Euler's totient φ(1580) = 624 numbers up to 1580 share no factor with it.
- 4
The digits of 1580 add up to 14, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 78 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1580 = 2^{2} \times 5 \times 79 \]1580 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 3360 |
| Euler totient φ(n) | 624 |
| Square | 2496400 |
| Cube | 3944312000 |
| Square root | 39.749214 (= 2√395) |
| Digit sum / digital root | 14 / 5 |
| Collatz steps to 1 | 78 |
| Scientific notation | 1.58 × |
1580 in other forms
| Form | Value |
|---|---|
| In words | one thousand five hundred and eighty |
| Roman numerals | MDLXXX |
| Binary (base 2) | 11000101100 |
| Octal (base 8) | 3054 |
| Hexadecimal (base 16) | 62C |
| Base 3 | 2011112 |
| As time | 1580 seconds = 26 min 20 s |
Is 1580 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (1580 ÷ 2 = 790) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (1580 ÷ 4 = 395) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (1580 ÷ 5 = 316) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 2) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 5) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (1580 ÷ 10 = 158) | 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 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1580 a prime number?
No. 1580 = × 5 × 79, so it is divisible by 2.
What are the factors of 1580?
1, 2, 4, 5, 10, 20, 79, 158, 316, 395, 790, 1580.
What is 1580 in binary?
11000101100 (hexadecimal 62C, octal 3054).
What is the square root of 1580?
About 39.7492, exactly 2√395.
What is 1580 in Roman numerals?
MDLXXX.
Is 1580 divisible by 3?
No. Its digits add up to 14, which is not a multiple of 3.
What is special about the number 1580?
It is a composite number with 12 divisors.