The number 42120
42120 is a composite number with 80 divisors. Its prime factorisation is × × 5 × 13. Divisors (80): 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 15, 18, 20, 24, 26 … 42120.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 42120: a Harshad number: divisible by its digit sum 9.
- 2
42120 is composite. Its prime factorisation is
- 3
The divisors add up to 152460; without 42120 itself that is 110340, so 42120 is abundant (110340 is more than 42120). Euler's totient φ(42120) = 10368 numbers up to 42120 share no factor with it.
- 4
The digits of 42120 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 44 steps to reach 1.
LaTeX source of the formulas on this page
\[ 42120 = 2^{3} \times 3^{4} \times 5 \times 13 \]42120 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 80 |
| Sum of divisors | 152460 |
| Euler totient φ(n) | 10368 |
| Square | 1774094400 |
| Cube | 74724856128000 |
| Square root | 205.231577 (= 18√130) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 44 |
| Scientific notation | 4.212 × |
42120 in other forms
| Form | Value |
|---|---|
| In words | forty-two thousand one hundred and twenty |
| Binary (base 2) | 1010010010001000 |
| Octal (base 8) | 122210 |
| Hexadecimal (base 16) | A488 |
| Base 3 | 2010210000 |
| As time | 42120 seconds = 11 h 42 min 0 s |
Is 42120 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (42120 ÷ 2 = 21060) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (42120 ÷ 3 = 14040) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (42120 ÷ 4 = 10530) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (42120 ÷ 5 = 8424) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (42120 ÷ 6 = 7020) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 1) | 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 (42120 ÷ 8 = 5265) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (42120 ÷ 9 = 4680) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (42120 ÷ 10 = 4212) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (42120 ÷ 12 = 3510) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 42120 a prime number?
No. 42120 = × × 5 × 13, so it is divisible by 2.
What are the factors of 42120?
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 15, 18, 20, 24, 26, 27, 30, 36, 39, 40, 45, 52, 54, 60, 65, 72, 78, 81, 90, 104, 108, 117, 120, 130, 135, 156, 162, 180, 195, 216, 234, 260, 270, 312, 324, 351, 360, 390, 405, 468, 520, 540, 585, 648, 702, 780, 810, 936, 1053, 1080, 1170, 1404, 1560, 1620, 1755, 2106, 2340, 2808, 3240, 3510, 4212, 4680, 5265, 7020, 8424, 10530, 14040, 21060, 42120.
What is 42120 in binary?
1010010010001000 (hexadecimal A488, octal 122210).
What is the square root of 42120?
About 205.2316, exactly 18√130.
Is 42120 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 42120?
42120 is a Harshad number: divisible by its digit sum 9.