The number 48420
48420 is a composite number with 36 divisors. Its prime factorisation is × × 5 × 269. Divisors (36): 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60 … 48420.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 48420: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.
- 2
48420 is composite. Its prime factorisation is
- 3
The divisors add up to 147420; without 48420 itself that is 99000, so 48420 is abundant (99000 is more than 48420). Euler's totient φ(48420) = 12864 numbers up to 48420 share no factor with it.
- 4
The digits of 48420 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 189 steps to reach 1.
LaTeX source of the formulas on this page
\[ 48420 = 2^{2} \times 3^{2} \times 5 \times 269 \]48420 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 147420 |
| Euler totient φ(n) | 12864 |
| Square | 2344496400 |
| Cube | 113520515688000 |
| Square root | 220.045450 (= 6√1345) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 189 |
| Scientific notation | 4.842 × |
48420 in other forms
| Form | Value |
|---|---|
| In words | forty-eight thousand four hundred and twenty |
| Binary (base 2) | 1011110100100100 |
| Octal (base 8) | 136444 |
| Hexadecimal (base 16) | BD24 |
| Base 3 | 2110102100 |
| As time | 48420 seconds = 13 h 27 min 0 s |
Is 48420 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (48420 ÷ 2 = 24210) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (48420 ÷ 3 = 16140) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (48420 ÷ 4 = 12105) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (48420 ÷ 5 = 9684) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (48420 ÷ 6 = 8070) | 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 | No (remainder 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (48420 ÷ 9 = 5380) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (48420 ÷ 10 = 4842) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 9) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (48420 ÷ 12 = 4035) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 48420 a prime number?
No. 48420 = × × 5 × 269, so it is divisible by 2.
What are the factors of 48420?
1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180, 269, 538, 807, 1076, 1345, 1614, 2421, 2690, 3228, 4035, 4842, 5380, 8070, 9684, 12105, 16140, 24210, 48420.
What is 48420 in binary?
1011110100100100 (hexadecimal BD24, octal 136444).
What is the square root of 48420?
About 220.0454, exactly 6√1345.
Is 48420 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 48420?
48420 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.