The number 1880
1880 is a composite number with 16 divisors. Its prime factorisation is × 5 × 47. Divisors (16): 1, 2, 4, 5, 8, 10, 20, 40, 47, 94, 188, 235, 376, 470, 940, 1880.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1880: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
1880 is composite. Its prime factorisation is
- 3
The divisors add up to 4320; without 1880 itself that is 2440, so 1880 is abundant (2440 is more than 1880). Euler's totient φ(1880) = 736 numbers up to 1880 share no factor with it.
- 4
The digits of 1880 add up to 17, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 130 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1880 = 2^{3} \times 5 \times 47 \]1880 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 4320 |
| Euler totient φ(n) | 736 |
| Square | 3534400 |
| Cube | 6644672000 |
| Square root | 43.358967 (= 2√470) |
| Digit sum / digital root | 17 / 8 |
| Collatz steps to 1 | 130 |
| Scientific notation | 1.88 × |
1880 in other forms
| Form | Value |
|---|---|
| In words | one thousand eight hundred and eighty |
| Roman numerals | MDCCCLXXX |
| Binary (base 2) | 11101011000 |
| Octal (base 8) | 3530 |
| Hexadecimal (base 16) | 758 |
| Base 3 | 2120122 |
| As time | 1880 seconds = 31 min 20 s |
Is 1880 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (1880 ÷ 2 = 940) | 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 (1880 ÷ 4 = 470) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (1880 ÷ 5 = 376) | 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 4) | 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 (1880 ÷ 8 = 235) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 8) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (1880 ÷ 10 = 188) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 10) | 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 1880 a prime number?
No. 1880 = × 5 × 47, so it is divisible by 2.
What are the factors of 1880?
1, 2, 4, 5, 8, 10, 20, 40, 47, 94, 188, 235, 376, 470, 940, 1880.
What is 1880 in binary?
11101011000 (hexadecimal 758, octal 3530).
What is the square root of 1880?
About 43.3590, exactly 2√470.
What is 1880 in Roman numerals?
MDCCCLXXX.
Is 1880 divisible by 3?
No. Its digits add up to 17, which is not a multiple of 3.
What is special about the number 1880?
1880 is a happy number: repeatedly adding the squares of its digits reaches 1.