The number 39200
39200 is a composite number with 54 divisors. Its prime factorisation is × × . Divisors (54): 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 25, 28, 32, 35, 40, 49 … 39200.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 39200: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 14.
- 2
39200 is composite. Its prime factorisation is
- 3
The divisors add up to 111321; without 39200 itself that is 72121, so 39200 is abundant (72121 is more than 39200). Euler's totient φ(39200) = 13440 numbers up to 39200 share no factor with it.
- 4
The digits of 39200 add up to 14, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 137 steps to reach 1.
LaTeX source of the formulas on this page
\[ 39200 = 2^{5} \times 5^{2} \times 7^{2} \]39200 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 54 |
| Sum of divisors | 111321 |
| Euler totient φ(n) | 13440 |
| Square | 1536640000 |
| Cube | 60236288000000 |
| Square root | 197.989899 (= 140√2) |
| Digit sum / digital root | 14 / 5 |
| Collatz steps to 1 | 137 |
| Scientific notation | 3.92 × |
39200 in other forms
| Form | Value |
|---|---|
| In words | thirty-nine thousand two hundred |
| Binary (base 2) | 1001100100100000 |
| Octal (base 8) | 114440 |
| Hexadecimal (base 16) | 9920 |
| Base 3 | 1222202212 |
| As time | 39200 seconds = 10 h 53 min 20 s |
Is 39200 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (39200 ÷ 2 = 19600) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (39200 ÷ 4 = 9800) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (39200 ÷ 5 = 7840) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 2) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (39200 ÷ 7 = 5600) | 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 (39200 ÷ 8 = 4900) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 5) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (39200 ÷ 10 = 3920) | 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 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 39200 a prime number?
No. 39200 = × × , so it is divisible by 2.
What are the factors of 39200?
1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 25, 28, 32, 35, 40, 49, 50, 56, 70, 80, 98, 100, 112, 140, 160, 175, 196, 200, 224, 245, 280, 350, 392, 400, 490, 560, 700, 784, 800, 980, 1120, 1225, 1400, 1568, 1960, 2450, 2800, 3920, 4900, 5600, 7840, 9800, 19600, 39200.
What is 39200 in binary?
1001100100100000 (hexadecimal 9920, octal 114440).
What is the square root of 39200?
About 197.9899, exactly 140√2.
Is 39200 divisible by 3?
No. Its digits add up to 14, which is not a multiple of 3.
What is special about the number 39200?
39200 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 14.