The number 1506
1506 is a composite number with 8 divisors. Its prime factorisation is 2 × 3 × 251. Divisors (8): 1, 2, 3, 6, 251, 502, 753, 1506.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
1506 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
1506 is composite. Its prime factorisation is
- 3
The divisors add up to 3024; without 1506 itself that is 1518, so 1506 is abundant (1518 is more than 1506). Euler's totient φ(1506) = 500 numbers up to 1506 share no factor with it.
- 4
The digits of 1506 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 21 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1506 = 2 \times 3 \times 251 \]
1506 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 8 |
| Sum of divisors | 3024 |
| Euler totient φ(n) | 500 |
| Square | 2268036 |
| Cube | 3415662216 |
| Square root | 38.807216 |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 21 |
| Scientific notation | 1.506 × |
1506 in other forms
| Form | Value |
|---|---|
| In words | one thousand five hundred and six |
| Roman numerals | MDVI |
| Binary (base 2) | 10111100010 |
| Octal (base 8) | 2742 |
| Hexadecimal (base 16) | 5E2 |
| Base 3 | 2001210 |
| As time | 1506 seconds = 25 min 6 s |
Is 1506 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (1506 ÷ 2 = 753) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (1506 ÷ 3 = 502) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 2) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 1) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (1506 ÷ 6 = 251) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 1) | 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 2) | 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 6) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 10) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 6) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1506 a prime number?
No. 1506 = 2 × 3 × 251, so it is divisible by 2.
What are the factors of 1506?
1, 2, 3, 6, 251, 502, 753, 1506.
What is 1506 in binary?
10111100010 (hexadecimal 5E2, octal 2742).
What is the square root of 1506?
About 38.8072.
What is 1506 in Roman numerals?
MDVI.
Is 1506 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 1506?
It is a composite number with 8 divisors.