The number 72002
72002 is a composite number with 16 divisors. Its prime factorisation is 2 × 7 × 37 × 139. Divisors (16): 1, 2, 7, 14, 37, 74, 139, 259, 278, 518, 973, 1946, 5143, 10286, 36001, 72002.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
72002 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
72002 is composite. Its prime factorisation is
- 3
The divisors add up to 127680; without 72002 itself that is 55678, so 72002 is deficient (55678 is less than 72002). Euler's totient φ(72002) = 29808 numbers up to 72002 share no factor with it.
- 4
The digits of 72002 add up to 11, and repeating that until one digit is left gives the digital root 2. The Collatz sequence (halve if even, else 3n+1) takes 218 steps to reach 1.
LaTeX source of the formulas on this page
\[ 72002 = 2 \times 7 \times 37 \times 139 \]
72002 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 127680 |
| Euler totient φ(n) | 29808 |
| Square | 5184288004 |
| Cube | 373279104864008 |
| Square root | 268.331884 |
| Digit sum / digital root | 11 / 2 |
| Collatz steps to 1 | 218 |
| Scientific notation | 7.2002 × |
72002 in other forms
| Form | Value |
|---|---|
| In words | seventy-two thousand and two |
| Binary (base 2) | 10001100101000010 |
| Octal (base 8) | 214502 |
| Hexadecimal (base 16) | 11942 |
| Base 3 | 10122202202 |
| As time | 72002 seconds = 20 h 0 min 2 s |
Is 72002 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (72002 ÷ 2 = 36001) | 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 | Yes (72002 ÷ 7 = 10286) | 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 2) | 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 7) | 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 72002 a prime number?
No. 72002 = 2 × 7 × 37 × 139, so it is divisible by 2.
What are the factors of 72002?
1, 2, 7, 14, 37, 74, 139, 259, 278, 518, 973, 1946, 5143, 10286, 36001, 72002.
What is 72002 in binary?
10001100101000010 (hexadecimal 11942, octal 214502).
What is the square root of 72002?
About 268.3319.
Is 72002 divisible by 3?
No. Its digits add up to 11, which is not a multiple of 3.
What is special about the number 72002?
It is a composite number with 16 divisors.