The number 1540
1540 is a triangular number: 1 + 2 + … + 55 = 1540. Its prime factorisation is × 5 × 7 × 11. Divisors (24): 1, 2, 4, 5, 7, 10, 11, 14, 20, 22, 28, 35, 44, 55, 70, 77 … 1540.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1540: a triangular number: 1 + 2 + … + 55 = 1540; a Harshad number: divisible by its digit sum 10.
- 2
1540 is composite. Its prime factorisation is
- 3
The divisors add up to 4032; without 1540 itself that is 2492, so 1540 is abundant (2492 is more than 1540). Euler's totient φ(1540) = 480 numbers up to 1540 share no factor with it.
- 4
The digits of 1540 add up to 10, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 34 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1540 = 2^{2} \times 5 \times 7 \times 11 \]1540 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 4032 |
| Euler totient φ(n) | 480 |
| Square | 2371600 |
| Cube | 3652264000 |
| Square root | 39.242834 (= 2√385) |
| Digit sum / digital root | 10 / 1 |
| Collatz steps to 1 | 34 |
| Scientific notation | 1.54 × |
1540 in other forms
| Form | Value |
|---|---|
| In words | one thousand five hundred and forty |
| Roman numerals | MDXL |
| Binary (base 2) | 11000000100 |
| Octal (base 8) | 3004 |
| Hexadecimal (base 16) | 604 |
| Base 3 | 2010001 |
| As time | 1540 seconds = 25 min 40 s |
Is 1540 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (1540 ÷ 2 = 770) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (1540 ÷ 4 = 385) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (1540 ÷ 5 = 308) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 4) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (1540 ÷ 7 = 220) | 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 1) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (1540 ÷ 10 = 154) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (1540 ÷ 11 = 140) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1540 a prime number?
No. 1540 = × 5 × 7 × 11, so it is divisible by 2.
What are the factors of 1540?
1, 2, 4, 5, 7, 10, 11, 14, 20, 22, 28, 35, 44, 55, 70, 77, 110, 140, 154, 220, 308, 385, 770, 1540.
What is 1540 in binary?
11000000100 (hexadecimal 604, octal 3004).
What is the square root of 1540?
About 39.2428, exactly 2√385.
What is 1540 in Roman numerals?
MDXL.
Is 1540 divisible by 3?
No. Its digits add up to 10, which is not a multiple of 3.
What is special about the number 1540?
1540 is a triangular number: 1 + 2 + … + 55 = 1540; a Harshad number: divisible by its digit sum 10.