The number 9968
9968 is a composite number with 20 divisors. Its prime factorisation is × 7 × 89. Divisors (20): 1, 2, 4, 7, 8, 14, 16, 28, 56, 89, 112, 178, 356, 623, 712, 1246 … 9968.
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How to work it out
- 1
What is special about 9968: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
9968 is composite. Its prime factorisation is
- 3
The divisors add up to 22320; without 9968 itself that is 12352, so 9968 is abundant (12352 is more than 9968). Euler's totient φ(9968) = 4224 numbers up to 9968 share no factor with it.
- 4
The digits of 9968 add up to 32, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 135 steps to reach 1.
LaTeX source of the formulas on this page
\[ 9968 = 2^{4} \times 7 \times 89 \]9968 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 20 |
| Sum of divisors | 22320 |
| Euler totient φ(n) | 4224 |
| Square | 99361024 |
| Cube | 990430687232 |
| Square root | 99.839872 (= 4√623) |
| Digit sum / digital root | 32 / 5 |
| Collatz steps to 1 | 135 |
| Scientific notation | 9.968 × |
9968 in other forms
| Form | Value |
|---|---|
| In words | nine thousand nine hundred and sixty-eight |
| Binary (base 2) | 10011011110000 |
| Octal (base 8) | 23360 |
| Hexadecimal (base 16) | 26F0 |
| Base 3 | 111200012 |
| As time | 9968 seconds = 2 h 46 min 8 s |
Is 9968 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (9968 ÷ 2 = 4984) | 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 | Yes (9968 ÷ 4 = 2492) | 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 | No (remainder 2) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (9968 ÷ 7 = 1424) | 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 (9968 ÷ 8 = 1246) | 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 8) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 2) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 9968 a prime number?
No. 9968 = × 7 × 89, so it is divisible by 2.
What are the factors of 9968?
1, 2, 4, 7, 8, 14, 16, 28, 56, 89, 112, 178, 356, 623, 712, 1246, 1424, 2492, 4984, 9968.
What is 9968 in binary?
10011011110000 (hexadecimal 26F0, octal 23360).
What is the square root of 9968?
About 99.8399, exactly 4√623.
Is 9968 divisible by 3?
No. Its digits add up to 32, which is not a multiple of 3.
What is special about the number 9968?
9968 is a happy number: repeatedly adding the squares of its digits reaches 1.