The number 10101
10101 is a palindrome: it reads 10101 backwards too. Its prime factorisation is 3 × 7 × 13 × 37. Divisors (16): 1, 3, 7, 13, 21, 37, 39, 91, 111, 259, 273, 481, 777, 1443, 3367, 10101.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 10101: a palindrome: it reads 10101 backwards too; a Harshad number: divisible by its digit sum 3.
- 2
10101 is composite. Its prime factorisation is
- 3
The divisors add up to 17024; without 10101 itself that is 6923, so 10101 is deficient (6923 is less than 10101). Euler's totient φ(10101) = 5184 numbers up to 10101 share no factor with it.
- 4
The digits of 10101 add up to 3, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 42 steps to reach 1.
LaTeX source of the formulas on this page
\[ 10101 = 3 \times 7 \times 13 \times 37 \]
10101 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 17024 |
| Euler totient φ(n) | 5184 |
| Square | 102030201 |
| Cube | 1030607060301 |
| Square root | 100.503731 |
| Digit sum / digital root | 3 / 3 |
| Collatz steps to 1 | 42 |
| Scientific notation | 1.0101 × |
10101 in other forms
| Form | Value |
|---|---|
| In words | ten thousand one hundred and one |
| Binary (base 2) | 10011101110101 |
| Octal (base 8) | 23565 |
| Hexadecimal (base 16) | 2775 |
| Base 3 | 111212010 |
| As time | 10101 seconds = 2 h 48 min 21 s |
Is 10101 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 (10101 ÷ 3 = 3367) | 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 1) | 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 (10101 ÷ 7 = 1443) | 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 3) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 1) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 3) | 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 10101 a prime number?
No. 10101 = 3 × 7 × 13 × 37, so it is divisible by 3.
What are the factors of 10101?
1, 3, 7, 13, 21, 37, 39, 91, 111, 259, 273, 481, 777, 1443, 3367, 10101.
What is 10101 in binary?
10011101110101 (hexadecimal 2775, octal 23565).
What is the square root of 10101?
About 100.5037.
Is 10101 divisible by 3?
Yes. Its digits add up to 3, a multiple of 3.
What is special about the number 10101?
10101 is a palindrome: it reads 10101 backwards too; a Harshad number: divisible by its digit sum 3.