The number 3744
3744 is a composite number with 36 divisors. Its prime factorisation is × × 13. Divisors (36): 1, 2, 3, 4, 6, 8, 9, 12, 13, 16, 18, 24, 26, 32, 36, 39 … 3744.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 3744: a Harshad number: divisible by its digit sum 18.
- 2
3744 is composite. Its prime factorisation is
- 3
The divisors add up to 11466; without 3744 itself that is 7722, so 3744 is abundant (7722 is more than 3744). Euler's totient φ(3744) = 1152 numbers up to 3744 share no factor with it.
- 4
The digits of 3744 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 25 steps to reach 1.
LaTeX source of the formulas on this page
\[ 3744 = 2^{5} \times 3^{2} \times 13 \]3744 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 11466 |
| Euler totient φ(n) | 1152 |
| Square | 14017536 |
| Cube | 52481654784 |
| Square root | 61.188234 (= 12√26) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 25 |
| Scientific notation | 3.744 × |
3744 in other forms
| Form | Value |
|---|---|
| In words | three thousand seven hundred and forty-four |
| Roman numerals | MMMDCCXLIV |
| Binary (base 2) | 111010100000 |
| Octal (base 8) | 7240 |
| Hexadecimal (base 16) | EA0 |
| Base 3 | 12010200 |
| As time | 3744 seconds = 1 h 2 min 24 s |
Is 3744 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (3744 ÷ 2 = 1872) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (3744 ÷ 3 = 1248) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (3744 ÷ 4 = 936) | 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 (3744 ÷ 6 = 624) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 (3744 ÷ 8 = 468) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (3744 ÷ 9 = 416) | 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 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (3744 ÷ 12 = 312) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 3744 a prime number?
No. 3744 = × × 13, so it is divisible by 2.
What are the factors of 3744?
1, 2, 3, 4, 6, 8, 9, 12, 13, 16, 18, 24, 26, 32, 36, 39, 48, 52, 72, 78, 96, 104, 117, 144, 156, 208, 234, 288, 312, 416, 468, 624, 936, 1248, 1872, 3744.
What is 3744 in binary?
111010100000 (hexadecimal EA0, octal 7240).
What is the square root of 3744?
About 61.1882, exactly 12√26.
What is 3744 in Roman numerals?
MMMDCCXLIV.
Is 3744 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 3744?
3744 is a Harshad number: divisible by its digit sum 18.