The number 20520
20520 is a composite number with 64 divisors. Its prime factorisation is × × 5 × 19. Divisors (64): 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 19, 20, 24, 27 … 20520.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 20520: a Harshad number: divisible by its digit sum 9.
- 2
20520 is composite. Its prime factorisation is
- 3
The divisors add up to 72000; without 20520 itself that is 51480, so 20520 is abundant (51480 is more than 20520). Euler's totient φ(20520) = 5184 numbers up to 20520 share no factor with it.
- 4
The digits of 20520 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
\[ 20520 = 2^{3} \times 3^{3} \times 5 \times 19 \]20520 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 64 |
| Sum of divisors | 72000 |
| Euler totient φ(n) | 5184 |
| Square | 421070400 |
| Cube | 8640364608000 |
| Square root | 143.248037 (= 6√570) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 56 |
| Scientific notation | 2.052 × |
20520 in other forms
| Form | Value |
|---|---|
| In words | twenty thousand five hundred and twenty |
| Binary (base 2) | 101000000101000 |
| Octal (base 8) | 50050 |
| Hexadecimal (base 16) | 5028 |
| Base 3 | 1001011000 |
| As time | 20520 seconds = 5 h 42 min 0 s |
Is 20520 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (20520 ÷ 2 = 10260) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (20520 ÷ 3 = 6840) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (20520 ÷ 4 = 5130) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (20520 ÷ 5 = 4104) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (20520 ÷ 6 = 3420) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 (20520 ÷ 8 = 2565) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (20520 ÷ 9 = 2280) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (20520 ÷ 10 = 2052) | 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 (20520 ÷ 12 = 1710) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 20520 a prime number?
No. 20520 = × × 5 × 19, so it is divisible by 2.
What are the factors of 20520?
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 19, 20, 24, 27, 30, 36, 38, 40, 45, 54, 57, 60, 72, 76, 90, 95, 108, 114, 120, 135, 152, 171, 180, 190, 216, 228, 270, 285, 342, 360, 380, 456, 513, 540, 570, 684, 760, 855, 1026, 1080, 1140, 1368, 1710, 2052, 2280, 2565, 3420, 4104, 5130, 6840, 10260, 20520.
What is 20520 in binary?
101000000101000 (hexadecimal 5028, octal 50050).
What is the square root of 20520?
About 143.2480, exactly 6√570.
Is 20520 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 20520?
20520 is a Harshad number: divisible by its digit sum 9.