The number 8002
8002 is a composite number with 4 divisors. Its prime factorisation is 2 × 4001. Divisors (4): 1, 2, 4001, 8002.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 8002: a happy number: repeatedly adding the squares of its digits reaches 1; a semiprime: 2 × 4001, the product of two primes.
- 2
8002 is composite. Its prime factorisation is
- 3
The divisors add up to 12006; without 8002 itself that is 4004, so 8002 is deficient (4004 is less than 8002). Euler's totient φ(8002) = 4000 numbers up to 8002 share no factor with it.
- 4
The digits of 8002 add up to 10, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 44 steps to reach 1.
LaTeX source of the formulas on this page
\[ 8002 = 2 \times 4001 \]
8002 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 4 |
| Sum of divisors | 12006 |
| Euler totient φ(n) | 4000 |
| Square | 64032004 |
| Cube | 512384096008 |
| Square root | 89.453899 |
| Digit sum / digital root | 10 / 1 |
| Collatz steps to 1 | 44 |
| Scientific notation | 8.002 × |
8002 in other forms
| Form | Value |
|---|---|
| In words | eight thousand and two |
| Binary (base 2) | 1111101000010 |
| Octal (base 8) | 17502 |
| Hexadecimal (base 16) | 1F42 |
| Base 3 | 101222101 |
| As time | 8002 seconds = 2 h 13 min 22 s |
Is 8002 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (8002 ÷ 2 = 4001) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | 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 4) | 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 1) | 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 | No (remainder 10) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 8002 a prime number?
No. 8002 = 2 × 4001, so it is divisible by 2.
What are the factors of 8002?
1, 2, 4001, 8002.
What is 8002 in binary?
1111101000010 (hexadecimal 1F42, octal 17502).
What is the square root of 8002?
About 89.4539.
Is 8002 divisible by 3?
No. Its digits add up to 10, which is not a multiple of 3.
What is special about the number 8002?
8002 is a happy number: repeatedly adding the squares of its digits reaches 1; a semiprime: 2 × 4001, the product of two primes.