The number 10080
10080 is a highly composite number: it has 72 divisors, more than any smaller number. Its prime factorisation is × × 5 × 7. Divisors (72): 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20 … 10080.
Pick any whole number from 1 to 100,000.
How to work it out
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What is special about 10080: a highly composite number: it has 72 divisors, more than any smaller number; a Harshad number: divisible by its digit sum 9.
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10080 is composite. Its prime factorisation is
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The divisors add up to 39312; without 10080 itself that is 29232, so 10080 is abundant (29232 is more than 10080). Euler's totient φ(10080) = 2304 numbers up to 10080 share no factor with it.
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The digits of 10080 add up to 9, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 42 steps to reach 1.
LaTeX source of the formulas on this page
\[ 10080 = 2^{5} \times 3^{2} \times 5 \times 7 \]10080 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 72 |
| Sum of divisors | 39312 |
| Euler totient φ(n) | 2304 |
| Square | 101606400 |
| Cube | 1024192512000 |
| Square root | 100.399203 (= 12√70) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 42 |
| Scientific notation | 1.008 × |
10080 in other forms
| Form | Value |
|---|---|
| In words | ten thousand and eighty |
| Binary (base 2) | 10011101100000 |
| Octal (base 8) | 23540 |
| Hexadecimal (base 16) | 2760 |
| Base 3 | 111211100 |
| As time | 10080 seconds = 2 h 48 min 0 s |
Is 10080 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (10080 ÷ 2 = 5040) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (10080 ÷ 3 = 3360) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (10080 ÷ 4 = 2520) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (10080 ÷ 5 = 2016) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (10080 ÷ 6 = 1680) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (10080 ÷ 7 = 1440) | 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 (10080 ÷ 8 = 1260) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (10080 ÷ 9 = 1120) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (10080 ÷ 10 = 1008) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (10080 ÷ 12 = 840) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 10080 a prime number?
No. 10080 = × × 5 × 7, so it is divisible by 2.
What are the factors of 10080?
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 28, 30, 32, 35, 36, 40, 42, 45, 48, 56, 60, 63, 70, 72, 80, 84, 90, 96, 105, 112, 120, 126, 140, 144, 160, 168, 180, 210, 224, 240, 252, 280, 288, 315, 336, 360, 420, 480, 504, 560, 630, 672, 720, 840, 1008, 1120, 1260, 1440, 1680, 2016, 2520, 3360, 5040, 10080.
What is 10080 in binary?
10011101100000 (hexadecimal 2760, octal 23540).
What is the square root of 10080?
About 100.3992, exactly 12√70.
Is 10080 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 10080?
10080 is a highly composite number: it has 72 divisors, more than any smaller number; a Harshad number: divisible by its digit sum 9.