The number 101
101 is a palindromic prime: it reads the same backwards and is prime, a twin prime (101 and 103 are both prime) and the 26th prime number. Its only divisors are 1 and 101.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 101: a palindromic prime: it reads the same backwards and is prime; a twin prime (101 and 103 are both prime); the 26th prime number; a palindrome: it reads 101 backwards too.
- 2
101 is prime, so its only factors are 1 and 101. It is the 26th prime; the next prime is 103 and the one before is 97.
- 3
The divisors add up to 102; without 101 itself that is 1, so 101 is deficient (1 is less than 101). Euler's totient φ(101) = 100 numbers up to 101 share no factor with it.
- 4
The digits of 101 add up to 2, and repeating that until one digit is left gives the digital root 2. The Collatz sequence (halve if even, else 3n+1) takes 25 steps to reach 1.
101 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 102 |
| Euler totient φ(n) | 100 |
| Square | 10201 |
| Cube | 1030301 |
| Square root | 10.049876 |
| Digit sum / digital root | 2 / 2 |
| Collatz steps to 1 | 25 |
| Scientific notation | 1.01 × |
101 in other forms
| Form | Value |
|---|---|
| In words | one hundred and one |
| Roman numerals | CI |
| Binary (base 2) | 1100101 |
| Octal (base 8) | 145 |
| Hexadecimal (base 16) | 65 |
| Base 3 | 10202 |
| As time | 101 seconds = 1 min 41 s |
Is 101 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 2) | 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 5) | 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 5) | 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 1) | 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 5) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 101 a prime number?
Yes. 101 is divisible only by 1 and itself.
What are the factors of 101?
1, 101.
What is 101 in binary?
1100101 (hexadecimal 65, octal 145).
What is the square root of 101?
About 10.0499.
What is 101 in Roman numerals?
CI.
Is 101 divisible by 3?
No. Its digits add up to 2, which is not a multiple of 3.
What is special about the number 101?
101 is a palindromic prime: it reads the same backwards and is prime; a twin prime (101 and 103 are both prime); the 26th prime number; a palindrome: it reads 101 backwards too.