The number 15120
15120 is a highly composite number: it has 80 divisors, more than any smaller number. Its prime factorisation is × × 5 × 7. Divisors (80): 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20 … 15120.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 15120: a highly composite number: it has 80 divisors, more than any smaller number; a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 9.
- 2
15120 is composite. Its prime factorisation is
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The divisors add up to 59520; without 15120 itself that is 44400, so 15120 is abundant (44400 is more than 15120). Euler's totient φ(15120) = 3456 numbers up to 15120 share no factor with it.
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The digits of 15120 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 40 steps to reach 1.
LaTeX source of the formulas on this page
\[ 15120 = 2^{4} \times 3^{3} \times 5 \times 7 \]15120 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 80 |
| Sum of divisors | 59520 |
| Euler totient φ(n) | 3456 |
| Square | 228614400 |
| Cube | 3456649728000 |
| Square root | 122.963409 (= 12√105) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 40 |
| Scientific notation | 1.512 × |
15120 in other forms
| Form | Value |
|---|---|
| In words | fifteen thousand one hundred and twenty |
| Binary (base 2) | 11101100010000 |
| Octal (base 8) | 35420 |
| Hexadecimal (base 16) | 3B10 |
| Base 3 | 202202000 |
| As time | 15120 seconds = 4 h 12 min 0 s |
Is 15120 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (15120 ÷ 2 = 7560) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (15120 ÷ 3 = 5040) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (15120 ÷ 4 = 3780) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (15120 ÷ 5 = 3024) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (15120 ÷ 6 = 2520) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (15120 ÷ 7 = 2160) | 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 (15120 ÷ 8 = 1890) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (15120 ÷ 9 = 1680) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (15120 ÷ 10 = 1512) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (15120 ÷ 12 = 1260) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 15120 a prime number?
No. 15120 = × × 5 × 7, so it is divisible by 2.
What are the factors of 15120?
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 27, 28, 30, 35, 36, 40, 42, 45, 48, 54, 56, 60, 63, 70, 72, 80, 84, 90, 105, 108, 112, 120, 126, 135, 140, 144, 168, 180, 189, 210, 216, 240, 252, 270, 280, 315, 336, 360, 378, 420, 432, 504, 540, 560, 630, 720, 756, 840, 945, 1008, 1080, 1260, 1512, 1680, 1890, 2160, 2520, 3024, 3780, 5040, 7560, 15120.
What is 15120 in binary?
11101100010000 (hexadecimal 3B10, octal 35420).
What is the square root of 15120?
About 122.9634, exactly 12√105.
Is 15120 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 15120?
15120 is a highly composite number: it has 80 divisors, more than any smaller number; a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 9.