The number 1564
1564 is a composite number with 12 divisors. Its prime factorisation is × 17 × 23. Divisors (12): 1, 2, 4, 17, 23, 34, 46, 68, 92, 391, 782, 1564.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
1564 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
1564 is composite. Its prime factorisation is
- 3
The divisors add up to 3024; without 1564 itself that is 1460, so 1564 is deficient (1460 is less than 1564). Euler's totient φ(1564) = 704 numbers up to 1564 share no factor with it.
- 4
The digits of 1564 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 122 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1564 = 2^{2} \times 17 \times 23 \]1564 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 3024 |
| Euler totient φ(n) | 704 |
| Square | 2446096 |
| Cube | 3825694144 |
| Square root | 39.547440 (= 2√391) |
| Digit sum / digital root | 16 / 7 |
| Collatz steps to 1 | 122 |
| Scientific notation | 1.564 × |
1564 in other forms
| Form | Value |
|---|---|
| In words | one thousand five hundred and sixty-four |
| Roman numerals | MDLXIV |
| Binary (base 2) | 11000011100 |
| Octal (base 8) | 3034 |
| Hexadecimal (base 16) | 61C |
| Base 3 | 2010221 |
| As time | 1564 seconds = 26 min 4 s |
Is 1564 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (1564 ÷ 2 = 782) | 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 (1564 ÷ 4 = 391) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 4) | 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 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 | No (remainder 4) | 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 4) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 2) | 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 1564 a prime number?
No. 1564 = × 17 × 23, so it is divisible by 2.
What are the factors of 1564?
1, 2, 4, 17, 23, 34, 46, 68, 92, 391, 782, 1564.
What is 1564 in binary?
11000011100 (hexadecimal 61C, octal 3034).
What is the square root of 1564?
About 39.5474, exactly 2√391.
What is 1564 in Roman numerals?
MDLXIV.
Is 1564 divisible by 3?
No. Its digits add up to 16, which is not a multiple of 3.
What is special about the number 1564?
It is a composite number with 12 divisors.