The number 1752
1752 is a composite number with 16 divisors. Its prime factorisation is × 3 × 73. Divisors (16): 1, 2, 3, 4, 6, 8, 12, 24, 73, 146, 219, 292, 438, 584, 876, 1752.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1752: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
1752 is composite. Its prime factorisation is
- 3
The divisors add up to 4440; without 1752 itself that is 2688, so 1752 is abundant (2688 is more than 1752). Euler's totient φ(1752) = 576 numbers up to 1752 share no factor with it.
- 4
The digits of 1752 add up to 15, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 55 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1752 = 2^{3} \times 3 \times 73 \]1752 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 4440 |
| Euler totient φ(n) | 576 |
| Square | 3069504 |
| Cube | 5377771008 |
| Square root | 41.856899 (= 2√438) |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 55 |
| Scientific notation | 1.752 × |
1752 in other forms
| Form | Value |
|---|---|
| In words | one thousand seven hundred and fifty-two |
| Roman numerals | MDCCLII |
| Binary (base 2) | 11011011000 |
| Octal (base 8) | 3330 |
| Hexadecimal (base 16) | 6D8 |
| Base 3 | 2101220 |
| As time | 1752 seconds = 29 min 12 s |
Is 1752 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (1752 ÷ 2 = 876) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (1752 ÷ 3 = 584) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (1752 ÷ 4 = 438) | 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 | Yes (1752 ÷ 6 = 292) | 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 | Yes (1752 ÷ 8 = 219) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 2) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (1752 ÷ 12 = 146) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1752 a prime number?
No. 1752 = × 3 × 73, so it is divisible by 2.
What are the factors of 1752?
1, 2, 3, 4, 6, 8, 12, 24, 73, 146, 219, 292, 438, 584, 876, 1752.
What is 1752 in binary?
11011011000 (hexadecimal 6D8, octal 3330).
What is the square root of 1752?
About 41.8569, exactly 2√438.
What is 1752 in Roman numerals?
MDCCLII.
Is 1752 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 1752?
1752 is a happy number: repeatedly adding the squares of its digits reaches 1.