The number 528
528 is a triangular number: 1 + 2 + … + 32 = 528. Its prime factorisation is × 3 × 11. Divisors (20): 1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 24, 33, 44, 48, 66, 88 … 528.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 528: a triangular number: 1 + 2 + … + 32 = 528.
- 2
528 is composite. Its prime factorisation is
- 3
The divisors add up to 1488; without 528 itself that is 960, so 528 is abundant (960 is more than 528). Euler's totient φ(528) = 160 numbers up to 528 share no factor with it.
- 4
The digits of 528 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
\[ 528 = 2^{4} \times 3 \times 11 \]528 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 20 |
| Sum of divisors | 1488 |
| Euler totient φ(n) | 160 |
| Square | 278784 |
| Cube | 147197952 |
| Square root | 22.978251 (= 4√33) |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 30 |
| Scientific notation | 5.28 × |
528 in other forms
| Form | Value |
|---|---|
| In words | five hundred and twenty-eight |
| Roman numerals | DXXVIII |
| Binary (base 2) | 1000010000 |
| Octal (base 8) | 1020 |
| Hexadecimal (base 16) | 210 |
| Base 3 | 201120 |
| As time | 528 seconds = 8 min 48 s |
Is 528 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (528 ÷ 2 = 264) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (528 ÷ 3 = 176) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (528 ÷ 4 = 132) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 3) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (528 ÷ 6 = 88) | 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 (528 ÷ 8 = 66) | 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 | No (remainder 8) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (528 ÷ 11 = 48) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (528 ÷ 12 = 44) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 528 a prime number?
No. 528 = × 3 × 11, so it is divisible by 2.
What are the factors of 528?
1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 24, 33, 44, 48, 66, 88, 132, 176, 264, 528.
What is 528 in binary?
1000010000 (hexadecimal 210, octal 1020).
What is the square root of 528?
About 22.9783, exactly 4√33.
What is 528 in Roman numerals?
DXXVIII.
Is 528 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 528?
528 is a triangular number: 1 + 2 + … + 32 = 528.