The number 12420
12420 is a composite number with 48 divisors. Its prime factorisation is × × 5 × 23. Divisors (48): 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 23, 27, 30, 36 … 12420.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 12420: a Harshad number: divisible by its digit sum 9.
- 2
12420 is composite. Its prime factorisation is
- 3
The divisors add up to 40320; without 12420 itself that is 27900, so 12420 is abundant (27900 is more than 12420). Euler's totient φ(12420) = 3168 numbers up to 12420 share no factor with it.
- 4
The digits of 12420 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 156 steps to reach 1.
LaTeX source of the formulas on this page
\[ 12420 = 2^{2} \times 3^{3} \times 5 \times 23 \]12420 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 40320 |
| Euler totient φ(n) | 3168 |
| Square | 154256400 |
| Cube | 1915864488000 |
| Square root | 111.445054 (= 6√345) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 156 |
| Scientific notation | 1.242 × |
12420 in other forms
| Form | Value |
|---|---|
| In words | twelve thousand four hundred and twenty |
| Binary (base 2) | 11000010000100 |
| Octal (base 8) | 30204 |
| Hexadecimal (base 16) | 3084 |
| Base 3 | 122001000 |
| As time | 12420 seconds = 3 h 27 min 0 s |
Is 12420 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (12420 ÷ 2 = 6210) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (12420 ÷ 3 = 4140) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (12420 ÷ 4 = 3105) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (12420 ÷ 5 = 2484) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (12420 ÷ 6 = 2070) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 | No (remainder 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (12420 ÷ 9 = 1380) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (12420 ÷ 10 = 1242) | 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 (12420 ÷ 12 = 1035) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 12420 a prime number?
No. 12420 = × × 5 × 23, so it is divisible by 2.
What are the factors of 12420?
1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 23, 27, 30, 36, 45, 46, 54, 60, 69, 90, 92, 108, 115, 135, 138, 180, 207, 230, 270, 276, 345, 414, 460, 540, 621, 690, 828, 1035, 1242, 1380, 2070, 2484, 3105, 4140, 6210, 12420.
What is 12420 in binary?
11000010000100 (hexadecimal 3084, octal 30204).
What is the square root of 12420?
About 111.4451, exactly 6√345.
Is 12420 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 12420?
12420 is a Harshad number: divisible by its digit sum 9.