The number 1987
1987 is the 300th prime number. Its only divisors are 1 and 1987.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1987: the 300th prime number.
- 2
1987 is prime, so its only factors are 1 and 1987. It is the 300th prime; the next prime is 1993 and the one before is 1979.
- 3
The divisors add up to 1988; without 1987 itself that is 1, so 1987 is deficient (1 is less than 1987). Euler's totient φ(1987) = 1986 numbers up to 1987 share no factor with it.
- 4
The digits of 1987 add up to 25, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 94 steps to reach 1.
1987 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 1988 |
| Euler totient φ(n) | 1986 |
| Square | 3948169 |
| Cube | 7845011803 |
| Square root | 44.575778 |
| Digit sum / digital root | 25 / 7 |
| Collatz steps to 1 | 94 |
| Scientific notation | 1.987 × |
1987 in other forms
| Form | Value |
|---|---|
| In words | one thousand nine hundred and eighty-seven |
| Roman numerals | MCMLXXXVII |
| Binary (base 2) | 11111000011 |
| Octal (base 8) | 3703 |
| Hexadecimal (base 16) | 7C3 |
| Base 3 | 2201121 |
| As time | 1987 seconds = 33 min 7 s |
Is 1987 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | No (remainder 1) | 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 | No (remainder 3) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 2) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 1) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 3) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 7) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 7) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 7) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 7) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1987 a prime number?
Yes. 1987 is divisible only by 1 and itself.
What are the factors of 1987?
1, 1987.
What is 1987 in binary?
11111000011 (hexadecimal 7C3, octal 3703).
What is the square root of 1987?
About 44.5758.
What is 1987 in Roman numerals?
MCMLXXXVII.
Is 1987 divisible by 3?
No. Its digits add up to 25, which is not a multiple of 3.
What is special about the number 1987?
1987 is the 300th prime number.