The number 103
103 is a twin prime (101 and 103 are both prime) and the 27th prime number. Its only divisors are 1 and 103.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 103: a twin prime (101 and 103 are both prime); the 27th prime number; a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
103 is prime, so its only factors are 1 and 103. It is the 27th prime; the next prime is 107 and the one before is 101.
- 3
The divisors add up to 104; without 103 itself that is 1, so 103 is deficient (1 is less than 103). Euler's totient φ(103) = 102 numbers up to 103 share no factor with it.
- 4
The digits of 103 add up to 4, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 87 steps to reach 1.
103 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 104 |
| Euler totient φ(n) | 102 |
| Square | 10609 |
| Cube | 1092727 |
| Square root | 10.148892 |
| Digit sum / digital root | 4 / 4 |
| Collatz steps to 1 | 87 |
| Scientific notation | 1.03 × |
103 in other forms
| Form | Value |
|---|---|
| In words | one hundred and three |
| Roman numerals | CIII |
| Binary (base 2) | 1100111 |
| Octal (base 8) | 147 |
| Hexadecimal (base 16) | 67 |
| Base 3 | 10211 |
| As time | 103 seconds = 1 min 43 s |
Is 103 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 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 3) | 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 1) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 7) | 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 3) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 7) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 103 a prime number?
Yes. 103 is divisible only by 1 and itself.
What are the factors of 103?
1, 103.
What is 103 in binary?
1100111 (hexadecimal 67, octal 147).
What is the square root of 103?
About 10.1489.
What is 103 in Roman numerals?
CIII.
Is 103 divisible by 3?
No. Its digits add up to 4, which is not a multiple of 3.
What is special about the number 103?
103 is a twin prime (101 and 103 are both prime); the 27th prime number; a happy number: repeatedly adding the squares of its digits reaches 1.