The number 1020
1020 is a composite number with 24 divisors. Its prime factorisation is × 3 × 5 × 17. Divisors (24): 1, 2, 3, 4, 5, 6, 10, 12, 15, 17, 20, 30, 34, 51, 60, 68 … 1020.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1020: a Harshad number: divisible by its digit sum 3.
- 2
1020 is composite. Its prime factorisation is
- 3
The divisors add up to 3024; without 1020 itself that is 2004, so 1020 is abundant (2004 is more than 1020). Euler's totient φ(1020) = 256 numbers up to 1020 share no factor with it.
- 4
The digits of 1020 add up to 3, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 49 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1020 = 2^{2} \times 3 \times 5 \times 17 \]1020 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 3024 |
| Euler totient φ(n) | 256 |
| Square | 1040400 |
| Cube | 1061208000 |
| Square root | 31.937439 (= 2√255) |
| Digit sum / digital root | 3 / 3 |
| Collatz steps to 1 | 49 |
| Scientific notation | 1.02 × |
1020 in other forms
| Form | Value |
|---|---|
| In words | one thousand and twenty |
| Roman numerals | MXX |
| Binary (base 2) | 1111111100 |
| Octal (base 8) | 1774 |
| Hexadecimal (base 16) | 3FC |
| Base 3 | 1101210 |
| As time | 1020 seconds = 17 min 0 s |
Is 1020 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (1020 ÷ 2 = 510) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (1020 ÷ 3 = 340) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (1020 ÷ 4 = 255) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (1020 ÷ 5 = 204) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (1020 ÷ 6 = 170) | 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 | 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 (1020 ÷ 10 = 102) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 8) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (1020 ÷ 12 = 85) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1020 a prime number?
No. 1020 = × 3 × 5 × 17, so it is divisible by 2.
What are the factors of 1020?
1, 2, 3, 4, 5, 6, 10, 12, 15, 17, 20, 30, 34, 51, 60, 68, 85, 102, 170, 204, 255, 340, 510, 1020.
What is 1020 in binary?
1111111100 (hexadecimal 3FC, octal 1774).
What is the square root of 1020?
About 31.9374, exactly 2√255.
What is 1020 in Roman numerals?
MXX.
Is 1020 divisible by 3?
Yes. Its digits add up to 3, a multiple of 3.
What is special about the number 1020?
1020 is a Harshad number: divisible by its digit sum 3.