The number 7488
7488 is a composite number with 42 divisors. Its prime factorisation is × × 13. Divisors (42): 1, 2, 3, 4, 6, 8, 9, 12, 13, 16, 18, 24, 26, 32, 36, 39 … 7488.
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How to work it out
- 1
What is special about 7488: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
7488 is composite. Its prime factorisation is
- 3
The divisors add up to 23114; without 7488 itself that is 15626, so 7488 is abundant (15626 is more than 7488). Euler's totient φ(7488) = 2304 numbers up to 7488 share no factor with it.
- 4
The digits of 7488 add up to 27, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 26 steps to reach 1.
LaTeX source of the formulas on this page
\[ 7488 = 2^{6} \times 3^{2} \times 13 \]7488 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 42 |
| Sum of divisors | 23114 |
| Euler totient φ(n) | 2304 |
| Square | 56070144 |
| Cube | 419853238272 |
| Square root | 86.533231 (= 24√13) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 26 |
| Scientific notation | 7.488 × |
7488 in other forms
| Form | Value |
|---|---|
| In words | seven thousand four hundred and eighty-eight |
| Binary (base 2) | 1110101000000 |
| Octal (base 8) | 16500 |
| Hexadecimal (base 16) | 1D40 |
| Base 3 | 101021100 |
| As time | 7488 seconds = 2 h 4 min 48 s |
Is 7488 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (7488 ÷ 2 = 3744) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (7488 ÷ 3 = 2496) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (7488 ÷ 4 = 1872) | 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 | Yes (7488 ÷ 6 = 1248) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 (7488 ÷ 8 = 936) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (7488 ÷ 9 = 832) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 8) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 8) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (7488 ÷ 12 = 624) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 7488 a prime number?
No. 7488 = × × 13, so it is divisible by 2.
What are the factors of 7488?
1, 2, 3, 4, 6, 8, 9, 12, 13, 16, 18, 24, 26, 32, 36, 39, 48, 52, 64, 72, 78, 96, 104, 117, 144, 156, 192, 208, 234, 288, 312, 416, 468, 576, 624, 832, 936, 1248, 1872, 2496, 3744, 7488.
What is 7488 in binary?
1110101000000 (hexadecimal 1D40, octal 16500).
What is the square root of 7488?
About 86.5332, exactly 24√13.
Is 7488 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 7488?
7488 is a happy number: repeatedly adding the squares of its digits reaches 1.