The number 7500
7500 is a composite number with 30 divisors. Its prime factorisation is × 3 × . Divisors (30): 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100 … 7500.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 7500: a Harshad number: divisible by its digit sum 12.
- 2
7500 is composite. Its prime factorisation is
- 3
The divisors add up to 21868; without 7500 itself that is 14368, so 7500 is abundant (14368 is more than 7500). Euler's totient φ(7500) = 2000 numbers up to 7500 share no factor with it.
- 4
The digits of 7500 add up to 12, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 176 steps to reach 1.
LaTeX source of the formulas on this page
\[ 7500 = 2^{2} \times 3 \times 5^{4} \]7500 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 30 |
| Sum of divisors | 21868 |
| Euler totient φ(n) | 2000 |
| Square | 56250000 |
| Cube | 421875000000 |
| Square root | 86.602540 (= 50√3) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 176 |
| Scientific notation | 7.5 × |
7500 in other forms
| Form | Value |
|---|---|
| In words | seven thousand five hundred |
| Binary (base 2) | 1110101001100 |
| Octal (base 8) | 16514 |
| Hexadecimal (base 16) | 1D4C |
| Base 3 | 101021210 |
| As time | 7500 seconds = 2 h 5 min 0 s |
Is 7500 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (7500 ÷ 2 = 3750) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (7500 ÷ 3 = 2500) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (7500 ÷ 4 = 1875) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (7500 ÷ 5 = 1500) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (7500 ÷ 6 = 1250) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 | No (remainder 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (7500 ÷ 10 = 750) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 9) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (7500 ÷ 12 = 625) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 7500 a prime number?
No. 7500 = × 3 × , so it is divisible by 2.
What are the factors of 7500?
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 125, 150, 250, 300, 375, 500, 625, 750, 1250, 1500, 1875, 2500, 3750, 7500.
What is 7500 in binary?
1110101001100 (hexadecimal 1D4C, octal 16514).
What is the square root of 7500?
About 86.6025, exactly 50√3.
Is 7500 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 7500?
7500 is a Harshad number: divisible by its digit sum 12.