The number 3480
3480 is a composite number with 32 divisors. Its prime factorisation is × 3 × 5 × 29. Divisors (32): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 29, 30, 40, 58 … 3480.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 3480: a Harshad number: divisible by its digit sum 15.
- 2
3480 is composite. Its prime factorisation is
- 3
The divisors add up to 10800; without 3480 itself that is 7320, so 3480 is abundant (7320 is more than 3480). Euler's totient φ(3480) = 896 numbers up to 3480 share no factor with it.
- 4
The digits of 3480 add up to 15, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 30 steps to reach 1.
LaTeX source of the formulas on this page
\[ 3480 = 2^{3} \times 3 \times 5 \times 29 \]3480 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 10800 |
| Euler totient φ(n) | 896 |
| Square | 12110400 |
| Cube | 42144192000 |
| Square root | 58.991525 (= 2√870) |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 30 |
| Scientific notation | 3.48 × |
3480 in other forms
| Form | Value |
|---|---|
| In words | three thousand four hundred and eighty |
| Roman numerals | MMMCDLXXX |
| Binary (base 2) | 110110011000 |
| Octal (base 8) | 6630 |
| Hexadecimal (base 16) | D98 |
| Base 3 | 11202220 |
| As time | 3480 seconds = 58 min 0 s |
Is 3480 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (3480 ÷ 2 = 1740) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (3480 ÷ 3 = 1160) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (3480 ÷ 4 = 870) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (3480 ÷ 5 = 696) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (3480 ÷ 6 = 580) | 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 | Yes (3480 ÷ 8 = 435) | 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 (3480 ÷ 10 = 348) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (3480 ÷ 12 = 290) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 3480 a prime number?
No. 3480 = × 3 × 5 × 29, so it is divisible by 2.
What are the factors of 3480?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 29, 30, 40, 58, 60, 87, 116, 120, 145, 174, 232, 290, 348, 435, 580, 696, 870, 1160, 1740, 3480.
What is 3480 in binary?
110110011000 (hexadecimal D98, octal 6630).
What is the square root of 3480?
About 58.9915, exactly 2√870.
What is 3480 in Roman numerals?
MMMCDLXXX.
Is 3480 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 3480?
3480 is a Harshad number: divisible by its digit sum 15.