The number 1300
1300 is a composite number with 18 divisors. Its prime factorisation is × × 13. Divisors (18): 1, 2, 4, 5, 10, 13, 20, 25, 26, 50, 52, 65, 100, 130, 260, 325 … 1300.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1300: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 4.
- 2
1300 is composite. Its prime factorisation is
- 3
The divisors add up to 3038; without 1300 itself that is 1738, so 1300 is abundant (1738 is more than 1300). Euler's totient φ(1300) = 480 numbers up to 1300 share no factor with it.
- 4
The digits of 1300 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 26 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1300 = 2^{2} \times 5^{2} \times 13 \]1300 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 18 |
| Sum of divisors | 3038 |
| Euler totient φ(n) | 480 |
| Square | 1690000 |
| Cube | 2197000000 |
| Square root | 36.055513 (= 10√13) |
| Digit sum / digital root | 4 / 4 |
| Collatz steps to 1 | 26 |
| Scientific notation | 1.3 × |
1300 in other forms
| Form | Value |
|---|---|
| In words | one thousand three hundred |
| Roman numerals | MCCC |
| Binary (base 2) | 10100010100 |
| Octal (base 8) | 2424 |
| Hexadecimal (base 16) | 514 |
| Base 3 | 1210011 |
| As time | 1300 seconds = 21 min 40 s |
Is 1300 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (1300 ÷ 2 = 650) | 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 | Yes (1300 ÷ 4 = 325) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (1300 ÷ 5 = 260) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 4) | 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 4) | 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 | Yes (1300 ÷ 10 = 130) | 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 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1300 a prime number?
No. 1300 = × × 13, so it is divisible by 2.
What are the factors of 1300?
1, 2, 4, 5, 10, 13, 20, 25, 26, 50, 52, 65, 100, 130, 260, 325, 650, 1300.
What is 1300 in binary?
10100010100 (hexadecimal 514, octal 2424).
What is the square root of 1300?
About 36.0555, exactly 10√13.
What is 1300 in Roman numerals?
MCCC.
Is 1300 divisible by 3?
No. Its digits add up to 4, which is not a multiple of 3.
What is special about the number 1300?
1300 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 4.