The number 37648
37648 is a composite number with 20 divisors. Its prime factorisation is × 13 × 181. Divisors (20): 1, 2, 4, 8, 13, 16, 26, 52, 104, 181, 208, 362, 724, 1448, 2353, 2896 … 37648.
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How to work it out
- 1
37648 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
37648 is composite. Its prime factorisation is
- 3
The divisors add up to 78988; without 37648 itself that is 41340, so 37648 is abundant (41340 is more than 37648). Euler's totient φ(37648) = 17280 numbers up to 37648 share no factor with it.
- 4
The digits of 37648 add up to 28, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 36 steps to reach 1.
LaTeX source of the formulas on this page
\[ 37648 = 2^{4} \times 13 \times 181 \]37648 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 20 |
| Sum of divisors | 78988 |
| Euler totient φ(n) | 17280 |
| Square | 1417371904 |
| Cube | 53361217441792 |
| Square root | 194.030925 (= 4√2353) |
| Digit sum / digital root | 28 / 1 |
| Collatz steps to 1 | 36 |
| Scientific notation | 3.7648 × |
37648 in other forms
| Form | Value |
|---|---|
| In words | thirty-seven thousand six hundred and forty-eight |
| Binary (base 2) | 1001001100010000 |
| Octal (base 8) | 111420 |
| Hexadecimal (base 16) | 9310 |
| Base 3 | 1220122101 |
| As time | 37648 seconds = 10 h 27 min 28 s |
Is 37648 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (37648 ÷ 2 = 18824) | 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 (37648 ÷ 4 = 9412) | 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 | No (remainder 4) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 (37648 ÷ 8 = 4706) | 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 | No (remainder 8) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 6) | 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 37648 a prime number?
No. 37648 = × 13 × 181, so it is divisible by 2.
What are the factors of 37648?
1, 2, 4, 8, 13, 16, 26, 52, 104, 181, 208, 362, 724, 1448, 2353, 2896, 4706, 9412, 18824, 37648.
What is 37648 in binary?
1001001100010000 (hexadecimal 9310, octal 111420).
What is the square root of 37648?
About 194.0309, exactly 4√2353.
Is 37648 divisible by 3?
No. Its digits add up to 28, which is not a multiple of 3.
What is special about the number 37648?
It is a composite number with 20 divisors.