The number 3640
3640 is a composite number with 32 divisors. Its prime factorisation is × 5 × 7 × 13. Divisors (32): 1, 2, 4, 5, 7, 8, 10, 13, 14, 20, 26, 28, 35, 40, 52, 56 … 3640.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 3640: a Harshad number: divisible by its digit sum 13.
- 2
3640 is composite. Its prime factorisation is
- 3
The divisors add up to 10080; without 3640 itself that is 6440, so 3640 is abundant (6440 is more than 3640). Euler's totient φ(3640) = 1152 numbers up to 3640 share no factor with it.
- 4
The digits of 3640 add up to 13, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 43 steps to reach 1.
LaTeX source of the formulas on this page
\[ 3640 = 2^{3} \times 5 \times 7 \times 13 \]3640 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 10080 |
| Euler totient φ(n) | 1152 |
| Square | 13249600 |
| Cube | 48228544000 |
| Square root | 60.332413 (= 2√910) |
| Digit sum / digital root | 13 / 4 |
| Collatz steps to 1 | 43 |
| Scientific notation | 3.64 × |
3640 in other forms
| Form | Value |
|---|---|
| In words | three thousand six hundred and forty |
| Roman numerals | MMMDCXL |
| Binary (base 2) | 111000111000 |
| Octal (base 8) | 7070 |
| Hexadecimal (base 16) | E38 |
| Base 3 | 11222211 |
| As time | 3640 seconds = 1 h 0 min 40 s |
Is 3640 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (3640 ÷ 2 = 1820) | 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 (3640 ÷ 4 = 910) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (3640 ÷ 5 = 728) | 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 | Yes (3640 ÷ 7 = 520) | 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 (3640 ÷ 8 = 455) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 4) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (3640 ÷ 10 = 364) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 10) | 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 3640 a prime number?
No. 3640 = × 5 × 7 × 13, so it is divisible by 2.
What are the factors of 3640?
1, 2, 4, 5, 7, 8, 10, 13, 14, 20, 26, 28, 35, 40, 52, 56, 65, 70, 91, 104, 130, 140, 182, 260, 280, 364, 455, 520, 728, 910, 1820, 3640.
What is 3640 in binary?
111000111000 (hexadecimal E38, octal 7070).
What is the square root of 3640?
About 60.3324, exactly 2√910.
What is 3640 in Roman numerals?
MMMDCXL.
Is 3640 divisible by 3?
No. Its digits add up to 13, which is not a multiple of 3.
What is special about the number 3640?
3640 is a Harshad number: divisible by its digit sum 13.