The number 3900
3900 is a composite number with 36 divisors. Its prime factorisation is × 3 × × 13. Divisors (36): 1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 20, 25, 26, 30, 39, 50 … 3900.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 3900: a Harshad number: divisible by its digit sum 12.
- 2
3900 is composite. Its prime factorisation is
- 3
The divisors add up to 12152; without 3900 itself that is 8252, so 3900 is abundant (8252 is more than 3900). Euler's totient φ(3900) = 960 numbers up to 3900 share no factor with it.
- 4
The digits of 3900 add up to 12, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 144 steps to reach 1.
LaTeX source of the formulas on this page
\[ 3900 = 2^{2} \times 3 \times 5^{2} \times 13 \]3900 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 12152 |
| Euler totient φ(n) | 960 |
| Square | 15210000 |
| Cube | 59319000000 |
| Square root | 62.449980 (= 10√39) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 144 |
| Scientific notation | 3.9 × |
3900 in other forms
| Form | Value |
|---|---|
| In words | three thousand nine hundred |
| Roman numerals | MMMCM |
| Binary (base 2) | 111100111100 |
| Octal (base 8) | 7474 |
| Hexadecimal (base 16) | F3C |
| Base 3 | 12100110 |
| As time | 3900 seconds = 1 h 5 min 0 s |
Is 3900 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (3900 ÷ 2 = 1950) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (3900 ÷ 3 = 1300) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (3900 ÷ 4 = 975) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (3900 ÷ 5 = 780) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (3900 ÷ 6 = 650) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 1) | 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 | No (remainder 4) | 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 (3900 ÷ 10 = 390) | 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 | Yes (3900 ÷ 12 = 325) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 3900 a prime number?
No. 3900 = × 3 × × 13, so it is divisible by 2.
What are the factors of 3900?
1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 20, 25, 26, 30, 39, 50, 52, 60, 65, 75, 78, 100, 130, 150, 156, 195, 260, 300, 325, 390, 650, 780, 975, 1300, 1950, 3900.
What is 3900 in binary?
111100111100 (hexadecimal F3C, octal 7474).
What is the square root of 3900?
About 62.4500, exactly 10√39.
What is 3900 in Roman numerals?
MMMCM.
Is 3900 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 3900?
3900 is a Harshad number: divisible by its digit sum 12.