The number 97752
97752 is a composite number with 16 divisors. Its prime factorisation is × 3 × 4073. Divisors (16): 1, 2, 3, 4, 6, 8, 12, 24, 4073, 8146, 12219, 16292, 24438, 32584, 48876, 97752.
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How to work it out
- 1
What is special about 97752: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
97752 is composite. Its prime factorisation is
- 3
The divisors add up to 244440; without 97752 itself that is 146688, so 97752 is abundant (146688 is more than 97752). Euler's totient φ(97752) = 32576 numbers up to 97752 share no factor with it.
- 4
The digits of 97752 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 40 steps to reach 1.
LaTeX source of the formulas on this page
\[ 97752 = 2^{3} \times 3 \times 4073 \]97752 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 244440 |
| Euler totient φ(n) | 32576 |
| Square | 9555453504 |
| Cube | 934064690923008 |
| Square root | 312.653162 (= 2√24438) |
| Digit sum / digital root | 30 / 3 |
| Collatz steps to 1 | 40 |
| Scientific notation | 9.7752 × |
97752 in other forms
| Form | Value |
|---|---|
| In words | ninety-seven thousand seven hundred and fifty-two |
| Binary (base 2) | 10111110111011000 |
| Octal (base 8) | 276730 |
| Hexadecimal (base 16) | 17DD8 |
| Base 3 | 11222002110 |
| As time | 97752 seconds = 27 h 9 min 12 s |
Is 97752 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (97752 ÷ 2 = 48876) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (97752 ÷ 3 = 32584) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (97752 ÷ 4 = 24438) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 2) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (97752 ÷ 6 = 16292) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 (97752 ÷ 8 = 12219) | 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 2) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (97752 ÷ 12 = 8146) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 97752 a prime number?
No. 97752 = × 3 × 4073, so it is divisible by 2.
What are the factors of 97752?
1, 2, 3, 4, 6, 8, 12, 24, 4073, 8146, 12219, 16292, 24438, 32584, 48876, 97752.
What is 97752 in binary?
10111110111011000 (hexadecimal 17DD8, octal 276730).
What is the square root of 97752?
About 312.6532, exactly 2√24438.
Is 97752 divisible by 3?
Yes. Its digits add up to 30, a multiple of 3.
What is special about the number 97752?
97752 is a happy number: repeatedly adding the squares of its digits reaches 1.