The number 1760
1760 is a composite number with 24 divisors. Its prime factorisation is × 5 × 11. Divisors (24): 1, 2, 4, 5, 8, 10, 11, 16, 20, 22, 32, 40, 44, 55, 80, 88 … 1760.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1760: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
1760 is composite. Its prime factorisation is
- 3
The divisors add up to 4536; without 1760 itself that is 2776, so 1760 is abundant (2776 is more than 1760). Euler's totient φ(1760) = 640 numbers up to 1760 share no factor with it.
- 4
The digits of 1760 add up to 14, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 117 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1760 = 2^{5} \times 5 \times 11 \]1760 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 4536 |
| Euler totient φ(n) | 640 |
| Square | 3097600 |
| Cube | 5451776000 |
| Square root | 41.952354 (= 4√110) |
| Digit sum / digital root | 14 / 5 |
| Collatz steps to 1 | 117 |
| Scientific notation | 1.76 × |
1760 in other forms
| Form | Value |
|---|---|
| In words | one thousand seven hundred and sixty |
| Roman numerals | MDCCLX |
| Binary (base 2) | 11011100000 |
| Octal (base 8) | 3340 |
| Hexadecimal (base 16) | 6E0 |
| Base 3 | 2102012 |
| As time | 1760 seconds = 29 min 20 s |
Is 1760 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (1760 ÷ 2 = 880) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (1760 ÷ 4 = 440) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (1760 ÷ 5 = 352) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 2) | 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 (1760 ÷ 8 = 220) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 5) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (1760 ÷ 10 = 176) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (1760 ÷ 11 = 160) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1760 a prime number?
No. 1760 = × 5 × 11, so it is divisible by 2.
What are the factors of 1760?
1, 2, 4, 5, 8, 10, 11, 16, 20, 22, 32, 40, 44, 55, 80, 88, 110, 160, 176, 220, 352, 440, 880, 1760.
What is 1760 in binary?
11011100000 (hexadecimal 6E0, octal 3340).
What is the square root of 1760?
About 41.9524, exactly 4√110.
What is 1760 in Roman numerals?
MDCCLX.
Is 1760 divisible by 3?
No. Its digits add up to 14, which is not a multiple of 3.
What is special about the number 1760?
1760 is a happy number: repeatedly adding the squares of its digits reaches 1.