The number 4020
4020 is a composite number with 24 divisors. Its prime factorisation is × 3 × 5 × 67. Divisors (24): 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 67, 134, 201, 268 … 4020.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 4020: a Harshad number: divisible by its digit sum 6.
- 2
4020 is composite. Its prime factorisation is
- 3
The divisors add up to 11424; without 4020 itself that is 7404, so 4020 is abundant (7404 is more than 4020). Euler's totient φ(4020) = 1056 numbers up to 4020 share no factor with it.
- 4
The digits of 4020 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 69 steps to reach 1.
LaTeX source of the formulas on this page
\[ 4020 = 2^{2} \times 3 \times 5 \times 67 \]4020 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 11424 |
| Euler totient φ(n) | 1056 |
| Square | 16160400 |
| Cube | 64964808000 |
| Square root | 63.403470 (= 2√1005) |
| Digit sum / digital root | 6 / 6 |
| Collatz steps to 1 | 69 |
| Scientific notation | 4.02 × |
4020 in other forms
| Form | Value |
|---|---|
| In words | four thousand and twenty |
| Binary (base 2) | 111110110100 |
| Octal (base 8) | 7664 |
| Hexadecimal (base 16) | FB4 |
| Base 3 | 12111220 |
| As time | 4020 seconds = 1 h 7 min 0 s |
Is 4020 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (4020 ÷ 2 = 2010) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (4020 ÷ 3 = 1340) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (4020 ÷ 4 = 1005) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (4020 ÷ 5 = 804) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (4020 ÷ 6 = 670) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 6) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (4020 ÷ 10 = 402) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 5) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (4020 ÷ 12 = 335) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 4020 a prime number?
No. 4020 = × 3 × 5 × 67, so it is divisible by 2.
What are the factors of 4020?
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 67, 134, 201, 268, 335, 402, 670, 804, 1005, 1340, 2010, 4020.
What is 4020 in binary?
111110110100 (hexadecimal FB4, octal 7664).
What is the square root of 4020?
About 63.4035, exactly 2√1005.
Is 4020 divisible by 3?
Yes. Its digits add up to 6, a multiple of 3.
What is special about the number 4020?
4020 is a Harshad number: divisible by its digit sum 6.