The number 7968
7968 is a composite number with 24 divisors. Its prime factorisation is × 3 × 83. Divisors (24): 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 83, 96, 166, 249, 332 … 7968.
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How to work it out
- 1
What is special about 7968: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
7968 is composite. Its prime factorisation is
- 3
The divisors add up to 21168; without 7968 itself that is 13200, so 7968 is abundant (13200 is more than 7968). Euler's totient φ(7968) = 2624 numbers up to 7968 share no factor with it.
- 4
The digits of 7968 add up to 30, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 52 steps to reach 1.
LaTeX source of the formulas on this page
\[ 7968 = 2^{5} \times 3 \times 83 \]7968 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 21168 |
| Euler totient φ(n) | 2624 |
| Square | 63489024 |
| Cube | 505880543232 |
| Square root | 89.263654 (= 4√498) |
| Digit sum / digital root | 30 / 3 |
| Collatz steps to 1 | 52 |
| Scientific notation | 7.968 × |
7968 in other forms
| Form | Value |
|---|---|
| In words | seven thousand nine hundred and sixty-eight |
| Binary (base 2) | 1111100100000 |
| Octal (base 8) | 17440 |
| Hexadecimal (base 16) | 1F20 |
| Base 3 | 101221010 |
| As time | 7968 seconds = 2 h 12 min 48 s |
Is 7968 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (7968 ÷ 2 = 3984) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (7968 ÷ 3 = 2656) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (7968 ÷ 4 = 1992) | 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 (7968 ÷ 6 = 1328) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 (7968 ÷ 8 = 996) | 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 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (7968 ÷ 12 = 664) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 7968 a prime number?
No. 7968 = × 3 × 83, so it is divisible by 2.
What are the factors of 7968?
1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 83, 96, 166, 249, 332, 498, 664, 996, 1328, 1992, 2656, 3984, 7968.
What is 7968 in binary?
1111100100000 (hexadecimal 1F20, octal 17440).
What is the square root of 7968?
About 89.2637, exactly 4√498.
Is 7968 divisible by 3?
Yes. Its digits add up to 30, a multiple of 3.
What is special about the number 7968?
7968 is a happy number: repeatedly adding the squares of its digits reaches 1.