The number 1968
1968 is a composite number with 20 divisors. Its prime factorisation is × 3 × 41. Divisors (20): 1, 2, 3, 4, 6, 8, 12, 16, 24, 41, 48, 82, 123, 164, 246, 328 … 1968.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1968: a Harshad number: divisible by its digit sum 24.
- 2
1968 is composite. Its prime factorisation is
- 3
The divisors add up to 5208; without 1968 itself that is 3240, so 1968 is abundant (3240 is more than 1968). Euler's totient φ(1968) = 640 numbers up to 1968 share no factor with it.
- 4
The digits of 1968 add up to 24, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 50 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1968 = 2^{4} \times 3 \times 41 \]1968 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 20 |
| Sum of divisors | 5208 |
| Euler totient φ(n) | 640 |
| Square | 3873024 |
| Cube | 7622111232 |
| Square root | 44.362146 (= 4√123) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 50 |
| Scientific notation | 1.968 × |
1968 in other forms
| Form | Value |
|---|---|
| In words | one thousand nine hundred and sixty-eight |
| Roman numerals | MCMLXVIII |
| Binary (base 2) | 11110110000 |
| Octal (base 8) | 3660 |
| Hexadecimal (base 16) | 7B0 |
| Base 3 | 2200220 |
| As time | 1968 seconds = 32 min 48 s |
Is 1968 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (1968 ÷ 2 = 984) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (1968 ÷ 3 = 656) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (1968 ÷ 4 = 492) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 3) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (1968 ÷ 6 = 328) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 1) | 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 (1968 ÷ 8 = 246) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 8) | 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 | Yes (1968 ÷ 12 = 164) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1968 a prime number?
No. 1968 = × 3 × 41, so it is divisible by 2.
What are the factors of 1968?
1, 2, 3, 4, 6, 8, 12, 16, 24, 41, 48, 82, 123, 164, 246, 328, 492, 656, 984, 1968.
What is 1968 in binary?
11110110000 (hexadecimal 7B0, octal 3660).
What is the square root of 1968?
About 44.3621, exactly 4√123.
What is 1968 in Roman numerals?
MCMLXVIII.
Is 1968 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 1968?
1968 is a Harshad number: divisible by its digit sum 24.