The number 4752
4752 is a composite number with 40 divisors. Its prime factorisation is × × 11. Divisors (40): 1, 2, 3, 4, 6, 8, 9, 11, 12, 16, 18, 22, 24, 27, 33, 36 … 4752.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 4752: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.
- 2
4752 is composite. Its prime factorisation is
- 3
The divisors add up to 14880; without 4752 itself that is 10128, so 4752 is abundant (10128 is more than 4752). Euler's totient φ(4752) = 1440 numbers up to 4752 share no factor with it.
- 4
The digits of 4752 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 77 steps to reach 1.
LaTeX source of the formulas on this page
\[ 4752 = 2^{4} \times 3^{3} \times 11 \]4752 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 40 |
| Sum of divisors | 14880 |
| Euler totient φ(n) | 1440 |
| Square | 22581504 |
| Cube | 107307307008 |
| Square root | 68.934752 (= 12√33) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 77 |
| Scientific notation | 4.752 × |
4752 in other forms
| Form | Value |
|---|---|
| In words | four thousand seven hundred and fifty-two |
| Binary (base 2) | 1001010010000 |
| Octal (base 8) | 11220 |
| Hexadecimal (base 16) | 1290 |
| Base 3 | 20112000 |
| As time | 4752 seconds = 1 h 19 min 12 s |
Is 4752 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (4752 ÷ 2 = 2376) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (4752 ÷ 3 = 1584) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (4752 ÷ 4 = 1188) | 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 (4752 ÷ 6 = 792) | 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 (4752 ÷ 8 = 594) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (4752 ÷ 9 = 528) | 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 | Yes (4752 ÷ 11 = 432) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (4752 ÷ 12 = 396) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 4752 a prime number?
No. 4752 = × × 11, so it is divisible by 2.
What are the factors of 4752?
1, 2, 3, 4, 6, 8, 9, 11, 12, 16, 18, 22, 24, 27, 33, 36, 44, 48, 54, 66, 72, 88, 99, 108, 132, 144, 176, 198, 216, 264, 297, 396, 432, 528, 594, 792, 1188, 1584, 2376, 4752.
What is 4752 in binary?
1001010010000 (hexadecimal 1290, octal 11220).
What is the square root of 4752?
About 68.9348, exactly 12√33.
Is 4752 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 4752?
4752 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.