The number 67003
67003 is the 6676th prime number. Its only divisors are 1 and 67003.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 67003: the 6676th prime number; a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
67003 is prime, so its only factors are 1 and 67003. It is the 6676th prime; the next prime is 67021 and the one before is 66977.
- 3
The divisors add up to 67004; without 67003 itself that is 1, so 67003 is deficient (1 is less than 67003). Euler's totient φ(67003) = 67002 numbers up to 67003 share no factor with it.
- 4
The digits of 67003 add up to 16, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 143 steps to reach 1.
67003 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 67004 |
| Euler totient φ(n) | 67002 |
| Square | 4489402009 |
| Cube | 300803402809027 |
| Square root | 258.849377 |
| Digit sum / digital root | 16 / 7 |
| Collatz steps to 1 | 143 |
| Scientific notation | 6.7003 × |
67003 in other forms
| Form | Value |
|---|---|
| In words | sixty-seven thousand and three |
| Binary (base 2) | 10000010110111011 |
| Octal (base 8) | 202673 |
| Hexadecimal (base 16) | 105BB |
| Base 3 | 10101220121 |
| As time | 67003 seconds = 18 h 36 min 43 s |
Is 67003 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | No (remainder 1) | 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 3) | 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 | No (remainder 1) | 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 3) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 7) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 3) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 2) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 7) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 67003 a prime number?
Yes. 67003 is divisible only by 1 and itself.
What are the factors of 67003?
1, 67003.
What is 67003 in binary?
10000010110111011 (hexadecimal 105BB, octal 202673).
What is the square root of 67003?
About 258.8494.
Is 67003 divisible by 3?
No. Its digits add up to 16, which is not a multiple of 3.
What is special about the number 67003?
67003 is the 6676th prime number; a happy number: repeatedly adding the squares of its digits reaches 1.