The number 22008
22008 is a composite number with 32 divisors. Its prime factorisation is × 3 × 7 × 131. Divisors (32): 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 131 … 22008.
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How to work it out
- 1
What is special about 22008: a Harshad number: divisible by its digit sum 12.
- 2
22008 is composite. Its prime factorisation is
- 3
The divisors add up to 63360; without 22008 itself that is 41352, so 22008 is abundant (41352 is more than 22008). Euler's totient φ(22008) = 6240 numbers up to 22008 share no factor with it.
- 4
The digits of 22008 add up to 12, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 175 steps to reach 1.
LaTeX source of the formulas on this page
\[ 22008 = 2^{3} \times 3 \times 7 \times 131 \]22008 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 63360 |
| Euler totient φ(n) | 6240 |
| Square | 484352064 |
| Cube | 10659620224512 |
| Square root | 148.350935 (= 2√5502) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 175 |
| Scientific notation | 2.2008 × |
22008 in other forms
| Form | Value |
|---|---|
| In words | twenty-two thousand and eight |
| Binary (base 2) | 101010111111000 |
| Octal (base 8) | 52770 |
| Hexadecimal (base 16) | 55F8 |
| Base 3 | 1010012010 |
| As time | 22008 seconds = 6 h 6 min 48 s |
Is 22008 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (22008 ÷ 2 = 11004) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (22008 ÷ 3 = 7336) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (22008 ÷ 4 = 5502) | 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 (22008 ÷ 6 = 3668) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (22008 ÷ 7 = 3144) | 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 (22008 ÷ 8 = 2751) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | 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 8) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (22008 ÷ 12 = 1834) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 22008 a prime number?
No. 22008 = × 3 × 7 × 131, so it is divisible by 2.
What are the factors of 22008?
1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 131, 168, 262, 393, 524, 786, 917, 1048, 1572, 1834, 2751, 3144, 3668, 5502, 7336, 11004, 22008.
What is 22008 in binary?
101010111111000 (hexadecimal 55F8, octal 52770).
What is the square root of 22008?
About 148.3509, exactly 2√5502.
Is 22008 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 22008?
22008 is a Harshad number: divisible by its digit sum 12.