The number 1008
1008 is a composite number with 30 divisors. Its prime factorisation is × × 7. Divisors (30): 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 36 … 1008.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1008: a Harshad number: divisible by its digit sum 9.
- 2
1008 is composite. Its prime factorisation is
- 3
The divisors add up to 3224; without 1008 itself that is 2216, so 1008 is abundant (2216 is more than 1008). Euler's totient φ(1008) = 288 numbers up to 1008 share no factor with it.
- 4
The digits of 1008 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 111 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1008 = 2^{4} \times 3^{2} \times 7 \]1008 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 30 |
| Sum of divisors | 3224 |
| Euler totient φ(n) | 288 |
| Square | 1016064 |
| Cube | 1024192512 |
| Square root | 31.749016 (= 12√7) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 111 |
| Scientific notation | 1.008 × |
1008 in other forms
| Form | Value |
|---|---|
| In words | one thousand and eight |
| Roman numerals | MVIII |
| Binary (base 2) | 1111110000 |
| Octal (base 8) | 1760 |
| Hexadecimal (base 16) | 3F0 |
| Base 3 | 1101100 |
| As time | 1008 seconds = 16 min 48 s |
Is 1008 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (1008 ÷ 2 = 504) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (1008 ÷ 3 = 336) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (1008 ÷ 4 = 252) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 3) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (1008 ÷ 6 = 168) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (1008 ÷ 7 = 144) | 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 (1008 ÷ 8 = 126) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (1008 ÷ 9 = 112) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 8) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 7) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (1008 ÷ 12 = 84) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1008 a prime number?
No. 1008 = × × 7, so it is divisible by 2.
What are the factors of 1008?
1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 36, 42, 48, 56, 63, 72, 84, 112, 126, 144, 168, 252, 336, 504, 1008.
What is 1008 in binary?
1111110000 (hexadecimal 3F0, octal 1760).
What is the square root of 1008?
About 31.7490, exactly 12√7.
What is 1008 in Roman numerals?
MVIII.
Is 1008 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 1008?
1008 is a Harshad number: divisible by its digit sum 9.