The number 97572
97572 is a composite number with 24 divisors. Its prime factorisation is × 3 × 47 × 173. Divisors (24): 1, 2, 3, 4, 6, 12, 47, 94, 141, 173, 188, 282, 346, 519, 564, 692 … 97572.
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How to work it out
- 1
What is special about 97572: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
97572 is composite. Its prime factorisation is
- 3
The divisors add up to 233856; without 97572 itself that is 136284, so 97572 is abundant (136284 is more than 97572). Euler's totient φ(97572) = 31648 numbers up to 97572 share no factor with it.
- 4
The digits of 97572 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 71 steps to reach 1.
LaTeX source of the formulas on this page
\[ 97572 = 2^{2} \times 3 \times 47 \times 173 \]97572 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 233856 |
| Euler totient φ(n) | 31648 |
| Square | 9520295184 |
| Cube | 928914241693248 |
| Square root | 312.365171 (= 2√24393) |
| Digit sum / digital root | 30 / 3 |
| Collatz steps to 1 | 71 |
| Scientific notation | 9.7572 × |
97572 in other forms
| Form | Value |
|---|---|
| In words | ninety-seven thousand five hundred and seventy-two |
| Binary (base 2) | 10111110100100100 |
| Octal (base 8) | 276444 |
| Hexadecimal (base 16) | 17D24 |
| Base 3 | 11221211210 |
| As time | 97572 seconds = 27 h 6 min 12 s |
Is 97572 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (97572 ÷ 2 = 48786) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (97572 ÷ 3 = 32524) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (97572 ÷ 4 = 24393) | 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 (97572 ÷ 6 = 16262) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 | No (remainder 4) | 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 2) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (97572 ÷ 12 = 8131) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 97572 a prime number?
No. 97572 = × 3 × 47 × 173, so it is divisible by 2.
What are the factors of 97572?
1, 2, 3, 4, 6, 12, 47, 94, 141, 173, 188, 282, 346, 519, 564, 692, 1038, 2076, 8131, 16262, 24393, 32524, 48786, 97572.
What is 97572 in binary?
10111110100100100 (hexadecimal 17D24, octal 276444).
What is the square root of 97572?
About 312.3652, exactly 2√24393.
Is 97572 divisible by 3?
Yes. Its digits add up to 30, a multiple of 3.
What is special about the number 97572?
97572 is a happy number: repeatedly adding the squares of its digits reaches 1.