The number 54120
54120 is a composite number with 64 divisors. Its prime factorisation is × 3 × 5 × 11 × 41. Divisors (64): 1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 20, 22, 24, 30, 33 … 54120.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 54120: a Harshad number: divisible by its digit sum 12.
- 2
54120 is composite. Its prime factorisation is
- 3
The divisors add up to 181440; without 54120 itself that is 127320, so 54120 is abundant (127320 is more than 54120). Euler's totient φ(54120) = 12800 numbers up to 54120 share no factor with it.
- 4
The digits of 54120 add up to 12, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 140 steps to reach 1.
LaTeX source of the formulas on this page
\[ 54120 = 2^{3} \times 3 \times 5 \times 11 \times 41 \]54120 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 64 |
| Sum of divisors | 181440 |
| Euler totient φ(n) | 12800 |
| Square | 2928974400 |
| Cube | 158516094528000 |
| Square root | 232.637056 (= 2√13530) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 140 |
| Scientific notation | 5.412 × |
54120 in other forms
| Form | Value |
|---|---|
| In words | fifty-four thousand one hundred and twenty |
| Binary (base 2) | 1101001101101000 |
| Octal (base 8) | 151550 |
| Hexadecimal (base 16) | D368 |
| Base 3 | 2202020110 |
| As time | 54120 seconds = 15 h 2 min 0 s |
Is 54120 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (54120 ÷ 2 = 27060) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (54120 ÷ 3 = 18040) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (54120 ÷ 4 = 13530) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (54120 ÷ 5 = 10824) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (54120 ÷ 6 = 9020) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 (54120 ÷ 8 = 6765) | 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 (54120 ÷ 10 = 5412) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (54120 ÷ 11 = 4920) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (54120 ÷ 12 = 4510) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 54120 a prime number?
No. 54120 = × 3 × 5 × 11 × 41, so it is divisible by 2.
What are the factors of 54120?
1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 20, 22, 24, 30, 33, 40, 41, 44, 55, 60, 66, 82, 88, 110, 120, 123, 132, 164, 165, 205, 220, 246, 264, 328, 330, 410, 440, 451, 492, 615, 660, 820, 902, 984, 1230, 1320, 1353, 1640, 1804, 2255, 2460, 2706, 3608, 4510, 4920, 5412, 6765, 9020, 10824, 13530, 18040, 27060, 54120.
What is 54120 in binary?
1101001101101000 (hexadecimal D368, octal 151550).
What is the square root of 54120?
About 232.6371, exactly 2√13530.
Is 54120 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 54120?
54120 is a Harshad number: divisible by its digit sum 12.