The number 53
53 is the 16th prime number. Its only divisors are 1 and 53.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 53: the 16th prime number.
- 2
53 is prime, so its only factors are 1 and 53. It is the 16th prime; the next prime is 59 and the one before is 47.
- 3
The divisors add up to 54; without 53 itself that is 1, so 53 is deficient (1 is less than 53). Euler's totient φ(53) = 52 numbers up to 53 share no factor with it.
- 4
The digits of 53 add up to 8, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 11 steps to reach 1.
53 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 54 |
| Euler totient φ(n) | 52 |
| Square | 2809 |
| Cube | 148877 |
| Square root | 7.280110 |
| Digit sum / digital root | 8 / 8 |
| Collatz steps to 1 | 11 |
| Scientific notation | 5.3 × |
53 in other forms
| Form | Value |
|---|---|
| In words | fifty-three |
| Roman numerals | LIII |
| Binary (base 2) | 110101 |
| Octal (base 8) | 65 |
| Hexadecimal (base 16) | 35 |
| Base 3 | 1222 |
| As time | 53 seconds |
Is 53 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 3) | 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 4) | 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 8) | 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 9) | 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 53 a prime number?
Yes. 53 is divisible only by 1 and itself.
What are the factors of 53?
1, 53.
What is 53 in binary?
110101 (hexadecimal 35, octal 65).
What is the square root of 53?
About 7.2801.
What is 53 in Roman numerals?
LIII.
Is 53 divisible by 3?
No. Its digits add up to 8, which is not a multiple of 3.
What is special about the number 53?
53 is the 16th prime number.