The number 83013
83013 is a binary palindrome (10100010001000101). Its prime factorisation is 3 × 7 × 59 × 67. Divisors (16): 1, 3, 7, 21, 59, 67, 177, 201, 413, 469, 1239, 1407, 3953, 11859, 27671, 83013.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 83013: a binary palindrome (10100010001000101).
- 2
83013 is composite. Its prime factorisation is
- 3
The divisors add up to 130560; without 83013 itself that is 47547, so 83013 is deficient (47547 is less than 83013). Euler's totient φ(83013) = 45936 numbers up to 83013 share no factor with it.
- 4
The digits of 83013 add up to 15, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 45 steps to reach 1.
LaTeX source of the formulas on this page
\[ 83013 = 3 \times 7 \times 59 \times 67 \]
83013 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 130560 |
| Euler totient φ(n) | 45936 |
| Square | 6891158169 |
| Cube | 572055713083197 |
| Square root | 288.119767 |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 45 |
| Scientific notation | 8.3013 × |
83013 in other forms
| Form | Value |
|---|---|
| In words | eighty-three thousand and thirteen |
| Binary (base 2) | 10100010001000101 |
| Octal (base 8) | 242105 |
| Hexadecimal (base 16) | 14445 |
| Base 3 | 11012212120 |
| As time | 83013 seconds = 23 h 3 min 33 s |
Is 83013 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 | Yes (83013 ÷ 3 = 27671) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 1) | 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 3) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (83013 ÷ 7 = 11859) | 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 5) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | 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 7) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 9) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 83013 a prime number?
No. 83013 = 3 × 7 × 59 × 67, so it is divisible by 3.
What are the factors of 83013?
1, 3, 7, 21, 59, 67, 177, 201, 413, 469, 1239, 1407, 3953, 11859, 27671, 83013.
What is 83013 in binary?
10100010001000101 (hexadecimal 14445, octal 242105).
What is the square root of 83013?
About 288.1198.
Is 83013 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 83013?
83013 is a binary palindrome (10100010001000101).