The number 1967
1967 is a binary palindrome (11110101111). Its prime factorisation is 7 × 281. Divisors (4): 1, 7, 281, 1967.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1967: a binary palindrome (11110101111); a happy number: repeatedly adding the squares of its digits reaches 1; a semiprime: 7 × 281, the product of two primes.
- 2
1967 is composite. Its prime factorisation is
- 3
The divisors add up to 2256; without 1967 itself that is 289, so 1967 is deficient (289 is less than 1967). Euler's totient φ(1967) = 1680 numbers up to 1967 share no factor with it.
- 4
The digits of 1967 add up to 23, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 99 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1967 = 7 \times 281 \]
1967 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 4 |
| Sum of divisors | 2256 |
| Euler totient φ(n) | 1680 |
| Square | 3869089 |
| Cube | 7610498063 |
| Square root | 44.350874 |
| Digit sum / digital root | 23 / 5 |
| Collatz steps to 1 | 99 |
| Scientific notation | 1.967 × |
1967 in other forms
| Form | Value |
|---|---|
| In words | one thousand nine hundred and sixty-seven |
| Roman numerals | MCMLXVII |
| Binary (base 2) | 11110101111 |
| Octal (base 8) | 3657 |
| Hexadecimal (base 16) | 7AF |
| Base 3 | 2200212 |
| As time | 1967 seconds = 32 min 47 s |
Is 1967 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 2) | 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 5) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (1967 ÷ 7 = 281) | 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 7) | 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 | No (remainder 7) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 9) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 11) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1967 a prime number?
No. 1967 = 7 × 281, so it is divisible by 7.
What are the factors of 1967?
1, 7, 281, 1967.
What is 1967 in binary?
11110101111 (hexadecimal 7AF, octal 3657).
What is the square root of 1967?
About 44.3509.
What is 1967 in Roman numerals?
MCMLXVII.
Is 1967 divisible by 3?
No. Its digits add up to 23, which is not a multiple of 3.
What is special about the number 1967?
1967 is a binary palindrome (11110101111); a happy number: repeatedly adding the squares of its digits reaches 1; a semiprime: 7 × 281, the product of two primes.