The number 32200
32200 is a composite number with 48 divisors. Its prime factorisation is × × 7 × 23. Divisors (48): 1, 2, 4, 5, 7, 8, 10, 14, 20, 23, 25, 28, 35, 40, 46, 50 … 32200.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 32200: a Harshad number: divisible by its digit sum 7.
- 2
32200 is composite. Its prime factorisation is
- 3
The divisors add up to 89280; without 32200 itself that is 57080, so 32200 is abundant (57080 is more than 32200). Euler's totient φ(32200) = 10560 numbers up to 32200 share no factor with it.
- 4
The digits of 32200 add up to 7, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 72 steps to reach 1.
LaTeX source of the formulas on this page
\[ 32200 = 2^{3} \times 5^{2} \times 7 \times 23 \]32200 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 89280 |
| Euler totient φ(n) | 10560 |
| Square | 1036840000 |
| Cube | 33386248000000 |
| Square root | 179.443584 (= 10√322) |
| Digit sum / digital root | 7 / 7 |
| Collatz steps to 1 | 72 |
| Scientific notation | 3.22 × |
32200 in other forms
| Form | Value |
|---|---|
| In words | thirty-two thousand two hundred |
| Binary (base 2) | 111110111001000 |
| Octal (base 8) | 76710 |
| Hexadecimal (base 16) | 7DC8 |
| Base 3 | 1122011121 |
| As time | 32200 seconds = 8 h 56 min 40 s |
Is 32200 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (32200 ÷ 2 = 16100) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (32200 ÷ 4 = 8050) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (32200 ÷ 5 = 6440) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 4) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (32200 ÷ 7 = 4600) | 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 (32200 ÷ 8 = 4025) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 7) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (32200 ÷ 10 = 3220) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 32200 a prime number?
No. 32200 = × × 7 × 23, so it is divisible by 2.
What are the factors of 32200?
1, 2, 4, 5, 7, 8, 10, 14, 20, 23, 25, 28, 35, 40, 46, 50, 56, 70, 92, 100, 115, 140, 161, 175, 184, 200, 230, 280, 322, 350, 460, 575, 644, 700, 805, 920, 1150, 1288, 1400, 1610, 2300, 3220, 4025, 4600, 6440, 8050, 16100, 32200.
What is 32200 in binary?
111110111001000 (hexadecimal 7DC8, octal 76710).
What is the square root of 32200?
About 179.4436, exactly 10√322.
Is 32200 divisible by 3?
No. Its digits add up to 7, which is not a multiple of 3.
What is special about the number 32200?
32200 is a Harshad number: divisible by its digit sum 7.