The number 99120
99120 is a composite number with 80 divisors. Its prime factorisation is × 3 × 5 × 7 × 59. Divisors (80): 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24 … 99120.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 99120: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 21.
- 2
99120 is composite. Its prime factorisation is
- 3
The divisors add up to 357120; without 99120 itself that is 258000, so 99120 is abundant (258000 is more than 99120). Euler's totient φ(99120) = 22272 numbers up to 99120 share no factor with it.
- 4
The digits of 99120 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 190 steps to reach 1.
LaTeX source of the formulas on this page
\[ 99120 = 2^{4} \times 3 \times 5 \times 7 \times 59 \]99120 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 80 |
| Sum of divisors | 357120 |
| Euler totient φ(n) | 22272 |
| Square | 9824774400 |
| Cube | 973831638528000 |
| Square root | 314.833289 (= 4√6195) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 190 |
| Scientific notation | 9.912 × |
99120 in other forms
| Form | Value |
|---|---|
| In words | ninety-nine thousand one hundred and twenty |
| Binary (base 2) | 11000001100110000 |
| Octal (base 8) | 301460 |
| Hexadecimal (base 16) | 18330 |
| Base 3 | 12000222010 |
| As time | 99120 seconds = 27 h 32 min 0 s |
Is 99120 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (99120 ÷ 2 = 49560) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (99120 ÷ 3 = 33040) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (99120 ÷ 4 = 24780) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (99120 ÷ 5 = 19824) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (99120 ÷ 6 = 16520) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (99120 ÷ 7 = 14160) | 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 (99120 ÷ 8 = 12390) | 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 (99120 ÷ 10 = 9912) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 10) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (99120 ÷ 12 = 8260) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 99120 a prime number?
No. 99120 = × 3 × 5 × 7 × 59, so it is divisible by 2.
What are the factors of 99120?
1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 28, 30, 35, 40, 42, 48, 56, 59, 60, 70, 80, 84, 105, 112, 118, 120, 140, 168, 177, 210, 236, 240, 280, 295, 336, 354, 413, 420, 472, 560, 590, 708, 826, 840, 885, 944, 1180, 1239, 1416, 1652, 1680, 1770, 2065, 2360, 2478, 2832, 3304, 3540, 4130, 4720, 4956, 6195, 6608, 7080, 8260, 9912, 12390, 14160, 16520, 19824, 24780, 33040, 49560, 99120.
What is 99120 in binary?
11000001100110000 (hexadecimal 18330, octal 301460).
What is the square root of 99120?
About 314.8333, exactly 4√6195.
Is 99120 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 99120?
99120 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 21.