The number 51360
51360 is a triangular number: 1 + 2 + … + 320 = 51360. Its prime factorisation is × 3 × 5 × 107. Divisors (48): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40 … 51360.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 51360: a triangular number: 1 + 2 + … + 320 = 51360; a Harshad number: divisible by its digit sum 15.
- 2
51360 is composite. Its prime factorisation is
- 3
The divisors add up to 163296; without 51360 itself that is 111936, so 51360 is abundant (111936 is more than 51360). Euler's totient φ(51360) = 13568 numbers up to 51360 share no factor with it.
- 4
The digits of 51360 add up to 15, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 26 steps to reach 1.
LaTeX source of the formulas on this page
\[ 51360 = 2^{5} \times 3 \times 5 \times 107 \]51360 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 163296 |
| Euler totient φ(n) | 13568 |
| Square | 2637849600 |
| Cube | 135479955456000 |
| Square root | 226.627448 (= 4√3210) |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 26 |
| Scientific notation | 5.136 × |
51360 in other forms
| Form | Value |
|---|---|
| In words | fifty-one thousand three hundred and sixty |
| Binary (base 2) | 1100100010100000 |
| Octal (base 8) | 144240 |
| Hexadecimal (base 16) | C8A0 |
| Base 3 | 2121110020 |
| As time | 51360 seconds = 14 h 16 min 0 s |
Is 51360 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (51360 ÷ 2 = 25680) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (51360 ÷ 3 = 17120) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (51360 ÷ 4 = 12840) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (51360 ÷ 5 = 10272) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (51360 ÷ 6 = 8560) | 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 (51360 ÷ 8 = 6420) | 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 (51360 ÷ 10 = 5136) | 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 (51360 ÷ 12 = 4280) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 51360 a prime number?
No. 51360 = × 3 × 5 × 107, so it is divisible by 2.
What are the factors of 51360?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 80, 96, 107, 120, 160, 214, 240, 321, 428, 480, 535, 642, 856, 1070, 1284, 1605, 1712, 2140, 2568, 3210, 3424, 4280, 5136, 6420, 8560, 10272, 12840, 17120, 25680, 51360.
What is 51360 in binary?
1100100010100000 (hexadecimal C8A0, octal 144240).
What is the square root of 51360?
About 226.6274, exactly 4√3210.
Is 51360 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 51360?
51360 is a triangular number: 1 + 2 + … + 320 = 51360; a Harshad number: divisible by its digit sum 15.