The number 3420
3420 is a composite number with 36 divisors. Its prime factorisation is × × 5 × 19. Divisors (36): 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 19, 20, 30, 36, 38 … 3420.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 3420: a Harshad number: divisible by its digit sum 9.
- 2
3420 is composite. Its prime factorisation is
- 3
The divisors add up to 10920; without 3420 itself that is 7500, so 3420 is abundant (7500 is more than 3420). Euler's totient φ(3420) = 864 numbers up to 3420 share no factor with it.
- 4
The digits of 3420 add up to 9, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 56 steps to reach 1.
LaTeX source of the formulas on this page
\[ 3420 = 2^{2} \times 3^{2} \times 5 \times 19 \]3420 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 10920 |
| Euler totient φ(n) | 864 |
| Square | 11696400 |
| Cube | 40001688000 |
| Square root | 58.480766 (= 6√95) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 56 |
| Scientific notation | 3.42 × |
3420 in other forms
| Form | Value |
|---|---|
| In words | three thousand four hundred and twenty |
| Roman numerals | MMMCDXX |
| Binary (base 2) | 110101011100 |
| Octal (base 8) | 6534 |
| Hexadecimal (base 16) | D5C |
| Base 3 | 11200200 |
| As time | 3420 seconds = 57 min 0 s |
Is 3420 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (3420 ÷ 2 = 1710) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (3420 ÷ 3 = 1140) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (3420 ÷ 4 = 855) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (3420 ÷ 5 = 684) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (3420 ÷ 6 = 570) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 | Yes (3420 ÷ 9 = 380) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (3420 ÷ 10 = 342) | 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 | Yes (3420 ÷ 12 = 285) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 3420 a prime number?
No. 3420 = × × 5 × 19, so it is divisible by 2.
What are the factors of 3420?
1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 19, 20, 30, 36, 38, 45, 57, 60, 76, 90, 95, 114, 171, 180, 190, 228, 285, 342, 380, 570, 684, 855, 1140, 1710, 3420.
What is 3420 in binary?
110101011100 (hexadecimal D5C, octal 6534).
What is the square root of 3420?
About 58.4808, exactly 6√95.
What is 3420 in Roman numerals?
MMMCDXX.
Is 3420 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 3420?
3420 is a Harshad number: divisible by its digit sum 9.