The number 1353
1353 is a composite number with 8 divisors. Its prime factorisation is 3 × 11 × 41. Divisors (8): 1, 3, 11, 33, 41, 123, 451, 1353.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1353: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
1353 is composite. Its prime factorisation is
- 3
The divisors add up to 2016; without 1353 itself that is 663, so 1353 is deficient (663 is less than 1353). Euler's totient φ(1353) = 800 numbers up to 1353 share no factor with it.
- 4
The digits of 1353 add up to 12, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 39 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1353 = 3 \times 11 \times 41 \]
1353 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 8 |
| Sum of divisors | 2016 |
| Euler totient φ(n) | 800 |
| Square | 1830609 |
| Cube | 2476813977 |
| Square root | 36.783148 |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 39 |
| Scientific notation | 1.353 × |
1353 in other forms
| Form | Value |
|---|---|
| In words | one thousand three hundred and fifty-three |
| Roman numerals | MCCCLIII |
| Binary (base 2) | 10101001001 |
| Octal (base 8) | 2511 |
| Hexadecimal (base 16) | 549 |
| Base 3 | 1212010 |
| As time | 1353 seconds = 22 min 33 s |
Is 1353 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 | Yes (1353 ÷ 3 = 451) | 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 3) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 3) | 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 | Yes (1353 ÷ 11 = 123) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 9) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1353 a prime number?
No. 1353 = 3 × 11 × 41, so it is divisible by 3.
What are the factors of 1353?
1, 3, 11, 33, 41, 123, 451, 1353.
What is 1353 in binary?
10101001001 (hexadecimal 549, octal 2511).
What is the square root of 1353?
About 36.7831.
What is 1353 in Roman numerals?
MCCCLIII.
Is 1353 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 1353?
1353 is a happy number: repeatedly adding the squares of its digits reaches 1.