The number 1002
1002 is a composite number with 8 divisors. Its prime factorisation is 2 × 3 × 167. Divisors (8): 1, 2, 3, 6, 167, 334, 501, 1002.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1002: a Harshad number: divisible by its digit sum 3.
- 2
1002 is composite. Its prime factorisation is
- 3
The divisors add up to 2016; without 1002 itself that is 1014, so 1002 is abundant (1014 is more than 1002). Euler's totient φ(1002) = 332 numbers up to 1002 share no factor with it.
- 4
The digits of 1002 add up to 3, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 111 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1002 = 2 \times 3 \times 167 \]
1002 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 8 |
| Sum of divisors | 2016 |
| Euler totient φ(n) | 332 |
| Square | 1004004 |
| Cube | 1006012008 |
| Square root | 31.654384 |
| Digit sum / digital root | 3 / 3 |
| Collatz steps to 1 | 111 |
| Scientific notation | 1.002 × |
1002 in other forms
| Form | Value |
|---|---|
| In words | one thousand and two |
| Roman numerals | MII |
| Binary (base 2) | 1111101010 |
| Octal (base 8) | 1752 |
| Hexadecimal (base 16) | 3EA |
| Base 3 | 1101010 |
| As time | 1002 seconds = 16 min 42 s |
Is 1002 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (1002 ÷ 2 = 501) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (1002 ÷ 3 = 334) | 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 2) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (1002 ÷ 6 = 167) | 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 2) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 1) | 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 1002 a prime number?
No. 1002 = 2 × 3 × 167, so it is divisible by 2.
What are the factors of 1002?
1, 2, 3, 6, 167, 334, 501, 1002.
What is 1002 in binary?
1111101010 (hexadecimal 3EA, octal 1752).
What is the square root of 1002?
About 31.6544.
What is 1002 in Roman numerals?
MII.
Is 1002 divisible by 3?
Yes. Its digits add up to 3, a multiple of 3.
What is special about the number 1002?
1002 is a Harshad number: divisible by its digit sum 3.