The number 3002
3002 is a composite number with 8 divisors. Its prime factorisation is 2 × 19 × 79. Divisors (8): 1, 2, 19, 38, 79, 158, 1501, 3002.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 3002: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
3002 is composite. Its prime factorisation is
- 3
The divisors add up to 4800; without 3002 itself that is 1798, so 3002 is deficient (1798 is less than 3002). Euler's totient φ(3002) = 1404 numbers up to 3002 share no factor with it.
- 4
The digits of 3002 add up to 5, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 48 steps to reach 1.
LaTeX source of the formulas on this page
\[ 3002 = 2 \times 19 \times 79 \]
3002 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 8 |
| Sum of divisors | 4800 |
| Euler totient φ(n) | 1404 |
| Square | 9012004 |
| Cube | 27054036008 |
| Square root | 54.790510 |
| Digit sum / digital root | 5 / 5 |
| Collatz steps to 1 | 48 |
| Scientific notation | 3.002 × |
3002 in other forms
| Form | Value |
|---|---|
| In words | three thousand and two |
| Roman numerals | MMMII |
| Binary (base 2) | 101110111010 |
| Octal (base 8) | 5672 |
| Hexadecimal (base 16) | BBA |
| Base 3 | 11010012 |
| As time | 3002 seconds = 50 min 2 s |
Is 3002 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (3002 ÷ 2 = 1501) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | 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 | No (remainder 2) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 5) | 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 10) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 2) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 3002 a prime number?
No. 3002 = 2 × 19 × 79, so it is divisible by 2.
What are the factors of 3002?
1, 2, 19, 38, 79, 158, 1501, 3002.
What is 3002 in binary?
101110111010 (hexadecimal BBA, octal 5672).
What is the square root of 3002?
About 54.7905.
What is 3002 in Roman numerals?
MMMII.
Is 3002 divisible by 3?
No. Its digits add up to 5, which is not a multiple of 3.
What is special about the number 3002?
3002 is a happy number: repeatedly adding the squares of its digits reaches 1.