The number 39648
39648 is a composite number with 48 divisors. Its prime factorisation is × 3 × 7 × 59. Divisors (48): 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48 … 39648.
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How to work it out
- 1
39648 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
39648 is composite. Its prime factorisation is
- 3
The divisors add up to 120960; without 39648 itself that is 81312, so 39648 is abundant (81312 is more than 39648). Euler's totient φ(39648) = 11136 numbers up to 39648 share no factor with it.
- 4
The digits of 39648 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 137 steps to reach 1.
LaTeX source of the formulas on this page
\[ 39648 = 2^{5} \times 3 \times 7 \times 59 \]39648 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 120960 |
| Euler totient φ(n) | 11136 |
| Square | 1571963904 |
| Cube | 62325224865792 |
| Square root | 199.118055 (= 4√2478) |
| Digit sum / digital root | 30 / 3 |
| Collatz steps to 1 | 137 |
| Scientific notation | 3.9648 × |
39648 in other forms
| Form | Value |
|---|---|
| In words | thirty-nine thousand six hundred and forty-eight |
| Binary (base 2) | 1001101011100000 |
| Octal (base 8) | 115340 |
| Hexadecimal (base 16) | 9AE0 |
| Base 3 | 2000101110 |
| As time | 39648 seconds = 11 h 0 min 48 s |
Is 39648 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (39648 ÷ 2 = 19824) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (39648 ÷ 3 = 13216) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (39648 ÷ 4 = 9912) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 3) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (39648 ÷ 6 = 6608) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (39648 ÷ 7 = 5664) | 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 (39648 ÷ 8 = 4956) | 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 8) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (39648 ÷ 12 = 3304) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 39648 a prime number?
No. 39648 = × 3 × 7 × 59, so it is divisible by 2.
What are the factors of 39648?
1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48, 56, 59, 84, 96, 112, 118, 168, 177, 224, 236, 336, 354, 413, 472, 672, 708, 826, 944, 1239, 1416, 1652, 1888, 2478, 2832, 3304, 4956, 5664, 6608, 9912, 13216, 19824, 39648.
What is 39648 in binary?
1001101011100000 (hexadecimal 9AE0, octal 115340).
What is the square root of 39648?
About 199.1181, exactly 4√2478.
Is 39648 divisible by 3?
Yes. Its digits add up to 30, a multiple of 3.
What is special about the number 39648?
It is a composite number with 48 divisors.