The number 168
168 is a composite number with 16 divisors. Its prime factorisation is × 3 × 7. Divisors (16): 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
168 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
168 is composite. Its prime factorisation is
- 3
The divisors add up to 480; without 168 itself that is 312, so 168 is abundant (312 is more than 168). Euler's totient φ(168) = 48 numbers up to 168 share no factor with it.
- 4
The digits of 168 add up to 15, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 10 steps to reach 1.
LaTeX source of the formulas on this page
\[ 168 = 2^{3} \times 3 \times 7 \]168 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 480 |
| Euler totient φ(n) | 48 |
| Square | 28224 |
| Cube | 4741632 |
| Square root | 12.961481 (= 2√42) |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 10 |
| Scientific notation | 1.68 × |
168 in other forms
| Form | Value |
|---|---|
| In words | one hundred and sixty-eight |
| Roman numerals | CLXVIII |
| Binary (base 2) | 10101000 |
| Octal (base 8) | 250 |
| Hexadecimal (base 16) | A8 |
| Base 3 | 20020 |
| As time | 168 seconds = 2 min 48 s |
Is 168 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (168 ÷ 2 = 84) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (168 ÷ 3 = 56) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (168 ÷ 4 = 42) | 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 (168 ÷ 6 = 28) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (168 ÷ 7 = 24) | 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 (168 ÷ 8 = 21) | 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 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (168 ÷ 12 = 14) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 168 a prime number?
No. 168 = × 3 × 7, so it is divisible by 2.
What are the factors of 168?
1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168.
What is 168 in binary?
10101000 (hexadecimal A8, octal 250).
What is the square root of 168?
About 12.9615, exactly 2√42.
What is 168 in Roman numerals?
CLXVIII.
Is 168 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 168?
It is a composite number with 16 divisors.