The number 1512
1512 is a composite number with 32 divisors. Its prime factorisation is × × 7. Divisors (32): 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 27, 28, 36 … 1512.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1512: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 9.
- 2
1512 is composite. Its prime factorisation is
- 3
The divisors add up to 4800; without 1512 itself that is 3288, so 1512 is abundant (3288 is more than 1512). Euler's totient φ(1512) = 432 numbers up to 1512 share no factor with it.
- 4
The digits of 1512 add up to 9, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 109 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1512 = 2^{3} \times 3^{3} \times 7 \]1512 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 4800 |
| Euler totient φ(n) | 432 |
| Square | 2286144 |
| Cube | 3456649728 |
| Square root | 38.884444 (= 6√42) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 109 |
| Scientific notation | 1.512 × |
1512 in other forms
| Form | Value |
|---|---|
| In words | one thousand five hundred and twelve |
| Roman numerals | MDXII |
| Binary (base 2) | 10111101000 |
| Octal (base 8) | 2750 |
| Hexadecimal (base 16) | 5E8 |
| Base 3 | 2002000 |
| As time | 1512 seconds = 25 min 12 s |
Is 1512 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (1512 ÷ 2 = 756) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (1512 ÷ 3 = 504) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (1512 ÷ 4 = 378) | 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 | Yes (1512 ÷ 6 = 252) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (1512 ÷ 7 = 216) | 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 | Yes (1512 ÷ 8 = 189) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (1512 ÷ 9 = 168) | 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 5) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (1512 ÷ 12 = 126) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1512 a prime number?
No. 1512 = × × 7, so it is divisible by 2.
What are the factors of 1512?
1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 27, 28, 36, 42, 54, 56, 63, 72, 84, 108, 126, 168, 189, 216, 252, 378, 504, 756, 1512.
What is 1512 in binary?
10111101000 (hexadecimal 5E8, octal 2750).
What is the square root of 1512?
About 38.8844, exactly 6√42.
What is 1512 in Roman numerals?
MDXII.
Is 1512 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 1512?
1512 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 9.