The number 54960
54960 is a composite number with 40 divisors. Its prime factorisation is × 3 × 5 × 229. Divisors (40): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48 … 54960.
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How to work it out
- 1
What is special about 54960: a Harshad number: divisible by its digit sum 24.
- 2
54960 is composite. Its prime factorisation is
- 3
The divisors add up to 171120; without 54960 itself that is 116160, so 54960 is abundant (116160 is more than 54960). Euler's totient φ(54960) = 14592 numbers up to 54960 share no factor with it.
- 4
The digits of 54960 add up to 24, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 153 steps to reach 1.
LaTeX source of the formulas on this page
\[ 54960 = 2^{4} \times 3 \times 5 \times 229 \]54960 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 40 |
| Sum of divisors | 171120 |
| Euler totient φ(n) | 14592 |
| Square | 3020601600 |
| Cube | 166012263936000 |
| Square root | 234.435492 (= 4√3435) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 153 |
| Scientific notation | 5.496 × |
54960 in other forms
| Form | Value |
|---|---|
| In words | fifty-four thousand nine hundred and sixty |
| Binary (base 2) | 1101011010110000 |
| Octal (base 8) | 153260 |
| Hexadecimal (base 16) | D6B0 |
| Base 3 | 2210101120 |
| As time | 54960 seconds = 15 h 16 min 0 s |
Is 54960 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (54960 ÷ 2 = 27480) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (54960 ÷ 3 = 18320) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (54960 ÷ 4 = 13740) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (54960 ÷ 5 = 10992) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (54960 ÷ 6 = 9160) | 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 (54960 ÷ 8 = 6870) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (54960 ÷ 10 = 5496) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (54960 ÷ 12 = 4580) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 54960 a prime number?
No. 54960 = × 3 × 5 × 229, so it is divisible by 2.
What are the factors of 54960?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 229, 240, 458, 687, 916, 1145, 1374, 1832, 2290, 2748, 3435, 3664, 4580, 5496, 6870, 9160, 10992, 13740, 18320, 27480, 54960.
What is 54960 in binary?
1101011010110000 (hexadecimal D6B0, octal 153260).
What is the square root of 54960?
About 234.4355, exactly 4√3435.
Is 54960 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 54960?
54960 is a Harshad number: divisible by its digit sum 24.