The number 1344
1344 is a composite number with 28 divisors. Its prime factorisation is × 3 × 7. Divisors (28): 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48 … 1344.
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How to work it out
- 1
What is special about 1344: a Harshad number: divisible by its digit sum 12.
- 2
1344 is composite. Its prime factorisation is
- 3
The divisors add up to 4064; without 1344 itself that is 2720, so 1344 is abundant (2720 is more than 1344). Euler's totient φ(1344) = 384 numbers up to 1344 share no factor with it.
- 4
The digits of 1344 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 13 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1344 = 2^{6} \times 3 \times 7 \]1344 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 28 |
| Sum of divisors | 4064 |
| Euler totient φ(n) | 384 |
| Square | 1806336 |
| Cube | 2427715584 |
| Square root | 36.660606 (= 8√21) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 13 |
| Scientific notation | 1.344 × |
1344 in other forms
| Form | Value |
|---|---|
| In words | one thousand three hundred and forty-four |
| Roman numerals | MCCCXLIV |
| Binary (base 2) | 10101000000 |
| Octal (base 8) | 2500 |
| Hexadecimal (base 16) | 540 |
| Base 3 | 1211210 |
| As time | 1344 seconds = 22 min 24 s |
Is 1344 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (1344 ÷ 2 = 672) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (1344 ÷ 3 = 448) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (1344 ÷ 4 = 336) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 4) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (1344 ÷ 6 = 224) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (1344 ÷ 7 = 192) | 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 | Yes (1344 ÷ 8 = 168) | 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 4) | 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 | Yes (1344 ÷ 12 = 112) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1344 a prime number?
No. 1344 = × 3 × 7, so it is divisible by 2.
What are the factors of 1344?
1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48, 56, 64, 84, 96, 112, 168, 192, 224, 336, 448, 672, 1344.
What is 1344 in binary?
10101000000 (hexadecimal 540, octal 2500).
What is the square root of 1344?
About 36.6606, exactly 8√21.
What is 1344 in Roman numerals?
MCCCXLIV.
Is 1344 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 1344?
1344 is a Harshad number: divisible by its digit sum 12.