The number 38640
38640 is a composite number with 80 divisors. Its prime factorisation is × 3 × 5 × 7 × 23. Divisors (80): 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 23 … 38640.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 38640: a Harshad number: divisible by its digit sum 21.
- 2
38640 is composite. Its prime factorisation is
- 3
The divisors add up to 142848; without 38640 itself that is 104208, so 38640 is abundant (104208 is more than 38640). Euler's totient φ(38640) = 8448 numbers up to 38640 share no factor with it.
- 4
The digits of 38640 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 124 steps to reach 1.
LaTeX source of the formulas on this page
\[ 38640 = 2^{4} \times 3 \times 5 \times 7 \times 23 \]38640 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 80 |
| Sum of divisors | 142848 |
| Euler totient φ(n) | 8448 |
| Square | 1493049600 |
| Cube | 57691436544000 |
| Square root | 196.570598 (= 4√2415) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 124 |
| Scientific notation | 3.864 × |
38640 in other forms
| Form | Value |
|---|---|
| In words | thirty-eight thousand six hundred and forty |
| Binary (base 2) | 1001011011110000 |
| Octal (base 8) | 113360 |
| Hexadecimal (base 16) | 96F0 |
| Base 3 | 1222000010 |
| As time | 38640 seconds = 10 h 44 min 0 s |
Is 38640 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (38640 ÷ 2 = 19320) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (38640 ÷ 3 = 12880) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (38640 ÷ 4 = 9660) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (38640 ÷ 5 = 7728) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (38640 ÷ 6 = 6440) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (38640 ÷ 7 = 5520) | 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 (38640 ÷ 8 = 4830) | 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 | Yes (38640 ÷ 10 = 3864) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 8) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (38640 ÷ 12 = 3220) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 38640 a prime number?
No. 38640 = × 3 × 5 × 7 × 23, so it is divisible by 2.
What are the factors of 38640?
1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 23, 24, 28, 30, 35, 40, 42, 46, 48, 56, 60, 69, 70, 80, 84, 92, 105, 112, 115, 120, 138, 140, 161, 168, 184, 210, 230, 240, 276, 280, 322, 336, 345, 368, 420, 460, 483, 552, 560, 644, 690, 805, 840, 920, 966, 1104, 1288, 1380, 1610, 1680, 1840, 1932, 2415, 2576, 2760, 3220, 3864, 4830, 5520, 6440, 7728, 9660, 12880, 19320, 38640.
What is 38640 in binary?
1001011011110000 (hexadecimal 96F0, octal 113360).
What is the square root of 38640?
About 196.5706, exactly 4√2415.
Is 38640 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 38640?
38640 is a Harshad number: divisible by its digit sum 21.