The number 1575
1575 is a composite number with 18 divisors. Its prime factorisation is × × 7. Divisors (18): 1, 3, 5, 7, 9, 15, 21, 25, 35, 45, 63, 75, 105, 175, 225, 315 … 1575.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1575: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
1575 is composite. Its prime factorisation is
- 3
The divisors add up to 3224; without 1575 itself that is 1649, so 1575 is abundant (1649 is more than 1575). Euler's totient φ(1575) = 720 numbers up to 1575 share no factor with it.
- 4
The digits of 1575 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 60 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1575 = 3^{2} \times 5^{2} \times 7 \]1575 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 18 |
| Sum of divisors | 3224 |
| Euler totient φ(n) | 720 |
| Square | 2480625 |
| Cube | 3906984375 |
| Square root | 39.686270 (= 15√7) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 60 |
| Scientific notation | 1.575 × |
1575 in other forms
| Form | Value |
|---|---|
| In words | one thousand five hundred and seventy-five |
| Roman numerals | MDLXXV |
| Binary (base 2) | 11000100111 |
| Octal (base 8) | 3047 |
| Hexadecimal (base 16) | 627 |
| Base 3 | 2011100 |
| As time | 1575 seconds = 26 min 15 s |
Is 1575 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | No (remainder 1) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (1575 ÷ 3 = 525) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 3) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (1575 ÷ 5 = 315) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 3) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (1575 ÷ 7 = 225) | 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 7) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (1575 ÷ 9 = 175) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 5) | 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 3) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1575 a prime number?
No. 1575 = × × 7, so it is divisible by 3.
What are the factors of 1575?
1, 3, 5, 7, 9, 15, 21, 25, 35, 45, 63, 75, 105, 175, 225, 315, 525, 1575.
What is 1575 in binary?
11000100111 (hexadecimal 627, octal 3047).
What is the square root of 1575?
About 39.6863, exactly 15√7.
What is 1575 in Roman numerals?
MDLXXV.
Is 1575 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 1575?
1575 is a happy number: repeatedly adding the squares of its digits reaches 1.