The number 2520
2520 is a highly composite number: it has 48 divisors, more than any smaller number. Its prime factorisation is × × 5 × 7. Divisors (48): 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20, 21 … 2520.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 2520: a highly composite number: it has 48 divisors, more than any smaller number; a Harshad number: divisible by its digit sum 9.
- 2
2520 is composite. Its prime factorisation is
- 3
The divisors add up to 9360; without 2520 itself that is 6840, so 2520 is abundant (6840 is more than 2520). Euler's totient φ(2520) = 576 numbers up to 2520 share no factor with it.
- 4
The digits of 2520 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 40 steps to reach 1.
LaTeX source of the formulas on this page
\[ 2520 = 2^{3} \times 3^{2} \times 5 \times 7 \]2520 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 9360 |
| Euler totient φ(n) | 576 |
| Square | 6350400 |
| Cube | 16003008000 |
| Square root | 50.199602 (= 6√70) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 40 |
| Scientific notation | 2.52 × |
2520 in other forms
| Form | Value |
|---|---|
| In words | two thousand five hundred and twenty |
| Roman numerals | MMDXX |
| Binary (base 2) | 100111011000 |
| Octal (base 8) | 4730 |
| Hexadecimal (base 16) | 9D8 |
| Base 3 | 10110100 |
| As time | 2520 seconds = 42 min 0 s |
Is 2520 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (2520 ÷ 2 = 1260) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (2520 ÷ 3 = 840) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (2520 ÷ 4 = 630) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (2520 ÷ 5 = 504) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (2520 ÷ 6 = 420) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (2520 ÷ 7 = 360) | 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 (2520 ÷ 8 = 315) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (2520 ÷ 9 = 280) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (2520 ÷ 10 = 252) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (2520 ÷ 12 = 210) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 2520 a prime number?
No. 2520 = × × 5 × 7, so it is divisible by 2.
What are the factors of 2520?
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20, 21, 24, 28, 30, 35, 36, 40, 42, 45, 56, 60, 63, 70, 72, 84, 90, 105, 120, 126, 140, 168, 180, 210, 252, 280, 315, 360, 420, 504, 630, 840, 1260, 2520.
What is 2520 in binary?
100111011000 (hexadecimal 9D8, octal 4730).
What is the square root of 2520?
About 50.1996, exactly 6√70.
What is 2520 in Roman numerals?
MMDXX.
Is 2520 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 2520?
2520 is a highly composite number: it has 48 divisors, more than any smaller number; a Harshad number: divisible by its digit sum 9.