The number 13702
13702 is a composite number with 16 divisors. Its prime factorisation is 2 × 13 × 17 × 31. Divisors (16): 1, 2, 13, 17, 26, 31, 34, 62, 221, 403, 442, 527, 806, 1054, 6851, 13702.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 13702: a Harshad number: divisible by its digit sum 13.
- 2
13702 is composite. Its prime factorisation is
- 3
The divisors add up to 24192; without 13702 itself that is 10490, so 13702 is deficient (10490 is less than 13702). Euler's totient φ(13702) = 5760 numbers up to 13702 share no factor with it.
- 4
The digits of 13702 add up to 13, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 58 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13702 = 2 \times 13 \times 17 \times 31 \]
13702 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 24192 |
| Euler totient φ(n) | 5760 |
| Square | 187744804 |
| Cube | 2572479304408 |
| Square root | 117.055542 |
| Digit sum / digital root | 13 / 4 |
| Collatz steps to 1 | 58 |
| Scientific notation | 1.3702 × |
13702 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand seven hundred and two |
| Binary (base 2) | 11010110000110 |
| Octal (base 8) | 32606 |
| Hexadecimal (base 16) | 3586 |
| Base 3 | 200210111 |
| As time | 13702 seconds = 3 h 48 min 22 s |
Is 13702 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (13702 ÷ 2 = 6851) | 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 3) | 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 6) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 4) | 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 10) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 13702 a prime number?
No. 13702 = 2 × 13 × 17 × 31, so it is divisible by 2.
What are the factors of 13702?
1, 2, 13, 17, 26, 31, 34, 62, 221, 403, 442, 527, 806, 1054, 6851, 13702.
What is 13702 in binary?
11010110000110 (hexadecimal 3586, octal 32606).
What is the square root of 13702?
About 117.0555.
Is 13702 divisible by 3?
No. Its digits add up to 13, which is not a multiple of 3.
What is special about the number 13702?
13702 is a Harshad number: divisible by its digit sum 13.