The number 1337
1337 is a composite number with 4 divisors. Its prime factorisation is 7 × 191. Divisors (4): 1, 7, 191, 1337.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1337: a happy number: repeatedly adding the squares of its digits reaches 1; a semiprime: 7 × 191, the product of two primes.
- 2
1337 is composite. Its prime factorisation is
- 3
The divisors add up to 1536; without 1337 itself that is 199, so 1337 is deficient (199 is less than 1337). Euler's totient φ(1337) = 1140 numbers up to 1337 share no factor with it.
- 4
The digits of 1337 add up to 14, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 44 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1337 = 7 \times 191 \]
1337 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 4 |
| Sum of divisors | 1536 |
| Euler totient φ(n) | 1140 |
| Square | 1787569 |
| Cube | 2389979753 |
| Square root | 36.565011 |
| Digit sum / digital root | 14 / 5 |
| Collatz steps to 1 | 44 |
| Scientific notation | 1.337 × |
1337 in other forms
| Form | Value |
|---|---|
| In words | one thousand three hundred and thirty-seven |
| Roman numerals | MCCCXXXVII |
| Binary (base 2) | 10100111001 |
| Octal (base 8) | 2471 |
| Hexadecimal (base 16) | 539 |
| Base 3 | 1211112 |
| As time | 1337 seconds = 22 min 17 s |
Is 1337 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 2) | 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 | Yes (1337 ÷ 7 = 191) | 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 1) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 5) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 7) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 6) | 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 1337 a prime number?
No. 1337 = 7 × 191, so it is divisible by 7.
What are the factors of 1337?
1, 7, 191, 1337.
What is 1337 in binary?
10100111001 (hexadecimal 539, octal 2471).
What is the square root of 1337?
About 36.5650.
What is 1337 in Roman numerals?
MCCCXXXVII.
Is 1337 divisible by 3?
No. Its digits add up to 14, which is not a multiple of 3.
What is special about the number 1337?
1337 is a happy number: repeatedly adding the squares of its digits reaches 1; a semiprime: 7 × 191, the product of two primes.