The number 7560
7560 is a highly composite number: it has 64 divisors, more than any smaller number. Its prime factorisation is × × 5 × 7. Divisors (64): 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20, 21 … 7560.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 7560: a highly composite number: it has 64 divisors, more than any smaller number; a Harshad number: divisible by its digit sum 18.
- 2
7560 is composite. Its prime factorisation is
- 3
The divisors add up to 28800; without 7560 itself that is 21240, so 7560 is abundant (21240 is more than 7560). Euler's totient φ(7560) = 1728 numbers up to 7560 share no factor with it.
- 4
The digits of 7560 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 39 steps to reach 1.
LaTeX source of the formulas on this page
\[ 7560 = 2^{3} \times 3^{3} \times 5 \times 7 \]7560 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 64 |
| Sum of divisors | 28800 |
| Euler totient φ(n) | 1728 |
| Square | 57153600 |
| Cube | 432081216000 |
| Square root | 86.948260 (= 6√210) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 39 |
| Scientific notation | 7.56 × |
7560 in other forms
| Form | Value |
|---|---|
| In words | seven thousand five hundred and sixty |
| Binary (base 2) | 1110110001000 |
| Octal (base 8) | 16610 |
| Hexadecimal (base 16) | 1D88 |
| Base 3 | 101101000 |
| As time | 7560 seconds = 2 h 6 min 0 s |
Is 7560 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (7560 ÷ 2 = 3780) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (7560 ÷ 3 = 2520) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (7560 ÷ 4 = 1890) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (7560 ÷ 5 = 1512) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (7560 ÷ 6 = 1260) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (7560 ÷ 7 = 1080) | 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 (7560 ÷ 8 = 945) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (7560 ÷ 9 = 840) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (7560 ÷ 10 = 756) | 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 (7560 ÷ 12 = 630) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 7560 a prime number?
No. 7560 = × × 5 × 7, so it is divisible by 2.
What are the factors of 7560?
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20, 21, 24, 27, 28, 30, 35, 36, 40, 42, 45, 54, 56, 60, 63, 70, 72, 84, 90, 105, 108, 120, 126, 135, 140, 168, 180, 189, 210, 216, 252, 270, 280, 315, 360, 378, 420, 504, 540, 630, 756, 840, 945, 1080, 1260, 1512, 1890, 2520, 3780, 7560.
What is 7560 in binary?
1110110001000 (hexadecimal 1D88, octal 16610).
What is the square root of 7560?
About 86.9483, exactly 6√210.
Is 7560 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 7560?
7560 is a highly composite number: it has 64 divisors, more than any smaller number; a Harshad number: divisible by its digit sum 18.