The number 1524
1524 is a composite number with 12 divisors. Its prime factorisation is × 3 × 127. Divisors (12): 1, 2, 3, 4, 6, 12, 127, 254, 381, 508, 762, 1524.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1524: a Harshad number: divisible by its digit sum 12.
- 2
1524 is composite. Its prime factorisation is
- 3
The divisors add up to 3584; without 1524 itself that is 2060, so 1524 is abundant (2060 is more than 1524). Euler's totient φ(1524) = 504 numbers up to 1524 share no factor with it.
- 4
The digits of 1524 add up to 12, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 109 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1524 = 2^{2} \times 3 \times 127 \]1524 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 3584 |
| Euler totient φ(n) | 504 |
| Square | 2322576 |
| Cube | 3539605824 |
| Square root | 39.038443 (= 2√381) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 109 |
| Scientific notation | 1.524 × |
1524 in other forms
| Form | Value |
|---|---|
| In words | one thousand five hundred and twenty-four |
| Roman numerals | MDXXIV |
| Binary (base 2) | 10111110100 |
| Octal (base 8) | 2764 |
| Hexadecimal (base 16) | 5F4 |
| Base 3 | 2002110 |
| As time | 1524 seconds = 25 min 24 s |
Is 1524 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (1524 ÷ 2 = 762) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (1524 ÷ 3 = 508) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (1524 ÷ 4 = 381) | 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 | Yes (1524 ÷ 6 = 254) | 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 3) | 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 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (1524 ÷ 12 = 127) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1524 a prime number?
No. 1524 = × 3 × 127, so it is divisible by 2.
What are the factors of 1524?
1, 2, 3, 4, 6, 12, 127, 254, 381, 508, 762, 1524.
What is 1524 in binary?
10111110100 (hexadecimal 5F4, octal 2764).
What is the square root of 1524?
About 39.0384, exactly 2√381.
What is 1524 in Roman numerals?
MDXXIV.
Is 1524 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 1524?
1524 is a Harshad number: divisible by its digit sum 12.