The number 83772
83772 is a composite number with 36 divisors. Its prime factorisation is × × 13 × 179. Divisors (36): 1, 2, 3, 4, 6, 9, 12, 13, 18, 26, 36, 39, 52, 78, 117, 156 … 83772.
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How to work it out
- 1
83772 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
83772 is composite. Its prime factorisation is
- 3
The divisors add up to 229320; without 83772 itself that is 145548, so 83772 is abundant (145548 is more than 83772). Euler's totient φ(83772) = 25632 numbers up to 83772 share no factor with it.
- 4
The digits of 83772 add up to 27, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 89 steps to reach 1.
LaTeX source of the formulas on this page
\[ 83772 = 2^{2} \times 3^{2} \times 13 \times 179 \]83772 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 229320 |
| Euler totient φ(n) | 25632 |
| Square | 7017747984 |
| Cube | 587890784115648 |
| Square root | 289.433930 (= 6√2327) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 89 |
| Scientific notation | 8.3772 × |
83772 in other forms
| Form | Value |
|---|---|
| In words | eighty-three thousand seven hundred and seventy-two |
| Binary (base 2) | 10100011100111100 |
| Octal (base 8) | 243474 |
| Hexadecimal (base 16) | 1473C |
| Base 3 | 11020220200 |
| As time | 83772 seconds = 23 h 16 min 12 s |
Is 83772 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (83772 ÷ 2 = 41886) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (83772 ÷ 3 = 27924) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (83772 ÷ 4 = 20943) | 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 (83772 ÷ 6 = 13962) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 | Yes (83772 ÷ 9 = 9308) | 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 7) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (83772 ÷ 12 = 6981) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 83772 a prime number?
No. 83772 = × × 13 × 179, so it is divisible by 2.
What are the factors of 83772?
1, 2, 3, 4, 6, 9, 12, 13, 18, 26, 36, 39, 52, 78, 117, 156, 179, 234, 358, 468, 537, 716, 1074, 1611, 2148, 2327, 3222, 4654, 6444, 6981, 9308, 13962, 20943, 27924, 41886, 83772.
What is 83772 in binary?
10100011100111100 (hexadecimal 1473C, octal 243474).
What is the square root of 83772?
About 289.4339, exactly 6√2327.
Is 83772 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 83772?
It is a composite number with 36 divisors.