The number 5460
5460 is a triangular number: 1 + 2 + … + 104 = 5460. Its prime factorisation is × 3 × 5 × 7 × 13. Divisors (48): 1, 2, 3, 4, 5, 6, 7, 10, 12, 13, 14, 15, 20, 21, 26, 28 … 5460.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 5460: a triangular number: 1 + 2 + … + 104 = 5460; a Harshad number: divisible by its digit sum 15.
- 2
5460 is composite. Its prime factorisation is
- 3
The divisors add up to 18816; without 5460 itself that is 13356, so 5460 is abundant (13356 is more than 5460). Euler's totient φ(5460) = 1152 numbers up to 5460 share no factor with it.
- 4
The digits of 5460 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 15 steps to reach 1.
LaTeX source of the formulas on this page
\[ 5460 = 2^{2} \times 3 \times 5 \times 7 \times 13 \]5460 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 18816 |
| Euler totient φ(n) | 1152 |
| Square | 29811600 |
| Cube | 162771336000 |
| Square root | 73.891813 (= 2√1365) |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 15 |
| Scientific notation | 5.46 × |
5460 in other forms
| Form | Value |
|---|---|
| In words | five thousand four hundred and sixty |
| Binary (base 2) | 1010101010100 |
| Octal (base 8) | 12524 |
| Hexadecimal (base 16) | 1554 |
| Base 3 | 21111020 |
| As time | 5460 seconds = 1 h 31 min 0 s |
Is 5460 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (5460 ÷ 2 = 2730) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (5460 ÷ 3 = 1820) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (5460 ÷ 4 = 1365) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (5460 ÷ 5 = 1092) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (5460 ÷ 6 = 910) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (5460 ÷ 7 = 780) | 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 | No (remainder 6) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (5460 ÷ 10 = 546) | 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 (5460 ÷ 12 = 455) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 5460 a prime number?
No. 5460 = × 3 × 5 × 7 × 13, so it is divisible by 2.
What are the factors of 5460?
1, 2, 3, 4, 5, 6, 7, 10, 12, 13, 14, 15, 20, 21, 26, 28, 30, 35, 39, 42, 52, 60, 65, 70, 78, 84, 91, 105, 130, 140, 156, 182, 195, 210, 260, 273, 364, 390, 420, 455, 546, 780, 910, 1092, 1365, 1820, 2730, 5460.
What is 5460 in binary?
1010101010100 (hexadecimal 1554, octal 12524).
What is the square root of 5460?
About 73.8918, exactly 2√1365.
Is 5460 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 5460?
5460 is a triangular number: 1 + 2 + … + 104 = 5460; a Harshad number: divisible by its digit sum 15.