The number 3120
3120 is a composite number with 40 divisors. Its prime factorisation is × 3 × 5 × 13. Divisors (40): 1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 15, 16, 20, 24, 26, 30 … 3120.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 3120: a Harshad number: divisible by its digit sum 6.
- 2
3120 is composite. Its prime factorisation is
- 3
The divisors add up to 10416; without 3120 itself that is 7296, so 3120 is abundant (7296 is more than 3120). Euler's totient φ(3120) = 768 numbers up to 3120 share no factor with it.
- 4
The digits of 3120 add up to 6, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 123 steps to reach 1.
LaTeX source of the formulas on this page
\[ 3120 = 2^{4} \times 3 \times 5 \times 13 \]3120 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 40 |
| Sum of divisors | 10416 |
| Euler totient φ(n) | 768 |
| Square | 9734400 |
| Cube | 30371328000 |
| Square root | 55.856960 (= 4√195) |
| Digit sum / digital root | 6 / 6 |
| Collatz steps to 1 | 123 |
| Scientific notation | 3.12 × |
3120 in other forms
| Form | Value |
|---|---|
| In words | three thousand one hundred and twenty |
| Roman numerals | MMMCXX |
| Binary (base 2) | 110000110000 |
| Octal (base 8) | 6060 |
| Hexadecimal (base 16) | C30 |
| Base 3 | 11021120 |
| As time | 3120 seconds = 52 min 0 s |
Is 3120 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (3120 ÷ 2 = 1560) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (3120 ÷ 3 = 1040) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (3120 ÷ 4 = 780) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (3120 ÷ 5 = 624) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (3120 ÷ 6 = 520) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 (3120 ÷ 8 = 390) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (3120 ÷ 10 = 312) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 7) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (3120 ÷ 12 = 260) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 3120 a prime number?
No. 3120 = × 3 × 5 × 13, so it is divisible by 2.
What are the factors of 3120?
1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 15, 16, 20, 24, 26, 30, 39, 40, 48, 52, 60, 65, 78, 80, 104, 120, 130, 156, 195, 208, 240, 260, 312, 390, 520, 624, 780, 1040, 1560, 3120.
What is 3120 in binary?
110000110000 (hexadecimal C30, octal 6060).
What is the square root of 3120?
About 55.8570, exactly 4√195.
What is 3120 in Roman numerals?
MMMCXX.
Is 3120 divisible by 3?
Yes. Its digits add up to 6, a multiple of 3.
What is special about the number 3120?
3120 is a Harshad number: divisible by its digit sum 6.