The number 7504
7504 is a composite number with 20 divisors. Its prime factorisation is × 7 × 67. Divisors (20): 1, 2, 4, 7, 8, 14, 16, 28, 56, 67, 112, 134, 268, 469, 536, 938 … 7504.
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How to work it out
- 1
What is special about 7504: a Harshad number: divisible by its digit sum 16.
- 2
7504 is composite. Its prime factorisation is
- 3
The divisors add up to 16864; without 7504 itself that is 9360, so 7504 is abundant (9360 is more than 7504). Euler's totient φ(7504) = 3168 numbers up to 7504 share no factor with it.
- 4
The digits of 7504 add up to 16, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 26 steps to reach 1.
LaTeX source of the formulas on this page
\[ 7504 = 2^{4} \times 7 \times 67 \]7504 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 20 |
| Sum of divisors | 16864 |
| Euler totient φ(n) | 3168 |
| Square | 56310016 |
| Cube | 422550360064 |
| Square root | 86.625631 (= 4√469) |
| Digit sum / digital root | 16 / 7 |
| Collatz steps to 1 | 26 |
| Scientific notation | 7.504 × |
7504 in other forms
| Form | Value |
|---|---|
| In words | seven thousand five hundred and four |
| Binary (base 2) | 1110101010000 |
| Octal (base 8) | 16520 |
| Hexadecimal (base 16) | 1D50 |
| Base 3 | 101021221 |
| As time | 7504 seconds = 2 h 5 min 4 s |
Is 7504 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (7504 ÷ 2 = 3752) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (7504 ÷ 4 = 1876) | 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 | No (remainder 4) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (7504 ÷ 7 = 1072) | 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 (7504 ÷ 8 = 938) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 7) | 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 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 7504 a prime number?
No. 7504 = × 7 × 67, so it is divisible by 2.
What are the factors of 7504?
1, 2, 4, 7, 8, 14, 16, 28, 56, 67, 112, 134, 268, 469, 536, 938, 1072, 1876, 3752, 7504.
What is 7504 in binary?
1110101010000 (hexadecimal 1D50, octal 16520).
What is the square root of 7504?
About 86.6256, exactly 4√469.
Is 7504 divisible by 3?
No. Its digits add up to 16, which is not a multiple of 3.
What is special about the number 7504?
7504 is a Harshad number: divisible by its digit sum 16.