The number 5040
5040 is a highly composite number: it has 60 divisors, more than any smaller number and 7! (7 factorial). Its prime factorisation is × × 5 × 7. Divisors (60): 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20 … 5040.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 5040: a highly composite number: it has 60 divisors, more than any smaller number; 7! (7 factorial); a Harshad number: divisible by its digit sum 9.
- 2
5040 is composite. Its prime factorisation is
- 3
The divisors add up to 19344; without 5040 itself that is 14304, so 5040 is abundant (14304 is more than 5040). Euler's totient φ(5040) = 1152 numbers up to 5040 share no factor with it.
- 4
The digits of 5040 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 41 steps to reach 1.
LaTeX source of the formulas on this page
\[ 5040 = 2^{4} \times 3^{2} \times 5 \times 7 \]5040 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 60 |
| Sum of divisors | 19344 |
| Euler totient φ(n) | 1152 |
| Square | 25401600 |
| Cube | 128024064000 |
| Square root | 70.992957 (= 12√35) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 41 |
| Scientific notation | 5.04 × |
5040 in other forms
| Form | Value |
|---|---|
| In words | five thousand and forty |
| Binary (base 2) | 1001110110000 |
| Octal (base 8) | 11660 |
| Hexadecimal (base 16) | 13B0 |
| Base 3 | 20220200 |
| As time | 5040 seconds = 1 h 24 min 0 s |
Is 5040 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (5040 ÷ 2 = 2520) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (5040 ÷ 3 = 1680) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (5040 ÷ 4 = 1260) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (5040 ÷ 5 = 1008) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (5040 ÷ 6 = 840) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (5040 ÷ 7 = 720) | 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 (5040 ÷ 8 = 630) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (5040 ÷ 9 = 560) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (5040 ÷ 10 = 504) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 2) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (5040 ÷ 12 = 420) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 5040 a prime number?
No. 5040 = × × 5 × 7, so it is divisible by 2.
What are the factors of 5040?
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 28, 30, 35, 36, 40, 42, 45, 48, 56, 60, 63, 70, 72, 80, 84, 90, 105, 112, 120, 126, 140, 144, 168, 180, 210, 240, 252, 280, 315, 336, 360, 420, 504, 560, 630, 720, 840, 1008, 1260, 1680, 2520, 5040.
What is 5040 in binary?
1001110110000 (hexadecimal 13B0, octal 11660).
What is the square root of 5040?
About 70.9930, exactly 12√35.
Is 5040 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 5040?
5040 is a highly composite number: it has 60 divisors, more than any smaller number; 7! (7 factorial); a Harshad number: divisible by its digit sum 9.