The number 35200
35200 is a composite number with 48 divisors. Its prime factorisation is × × 11. Divisors (48): 1, 2, 4, 5, 8, 10, 11, 16, 20, 22, 25, 32, 40, 44, 50, 55 … 35200.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 35200: a Harshad number: divisible by its digit sum 10.
- 2
35200 is composite. Its prime factorisation is
- 3
The divisors add up to 94860; without 35200 itself that is 59660, so 35200 is abundant (59660 is more than 35200). Euler's totient φ(35200) = 12800 numbers up to 35200 share no factor with it.
- 4
The digits of 35200 add up to 10, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 98 steps to reach 1.
LaTeX source of the formulas on this page
\[ 35200 = 2^{7} \times 5^{2} \times 11 \]35200 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 94860 |
| Euler totient φ(n) | 12800 |
| Square | 1239040000 |
| Cube | 43614208000000 |
| Square root | 187.616630 (= 40√22) |
| Digit sum / digital root | 10 / 1 |
| Collatz steps to 1 | 98 |
| Scientific notation | 3.52 × |
35200 in other forms
| Form | Value |
|---|---|
| In words | thirty-five thousand two hundred |
| Binary (base 2) | 1000100110000000 |
| Octal (base 8) | 104600 |
| Hexadecimal (base 16) | 8980 |
| Base 3 | 1210021201 |
| As time | 35200 seconds = 9 h 46 min 40 s |
Is 35200 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (35200 ÷ 2 = 17600) | 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 (35200 ÷ 4 = 8800) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (35200 ÷ 5 = 7040) | 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 | 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 (35200 ÷ 8 = 4400) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 1) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (35200 ÷ 10 = 3520) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (35200 ÷ 11 = 3200) | 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 35200 a prime number?
No. 35200 = × × 11, so it is divisible by 2.
What are the factors of 35200?
1, 2, 4, 5, 8, 10, 11, 16, 20, 22, 25, 32, 40, 44, 50, 55, 64, 80, 88, 100, 110, 128, 160, 176, 200, 220, 275, 320, 352, 400, 440, 550, 640, 704, 800, 880, 1100, 1408, 1600, 1760, 2200, 3200, 3520, 4400, 7040, 8800, 17600, 35200.
What is 35200 in binary?
1000100110000000 (hexadecimal 8980, octal 104600).
What is the square root of 35200?
About 187.6166, exactly 40√22.
Is 35200 divisible by 3?
No. Its digits add up to 10, which is not a multiple of 3.
What is special about the number 35200?
35200 is a Harshad number: divisible by its digit sum 10.