The number 7440
7440 is a composite number with 40 divisors. Its prime factorisation is × 3 × 5 × 31. Divisors (40): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 31, 40 … 7440.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 7440: a Harshad number: divisible by its digit sum 15.
- 2
7440 is composite. Its prime factorisation is
- 3
The divisors add up to 23808; without 7440 itself that is 16368, so 7440 is abundant (16368 is more than 7440). Euler's totient φ(7440) = 1920 numbers up to 7440 share no factor with it.
- 4
The digits of 7440 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 39 steps to reach 1.
LaTeX source of the formulas on this page
\[ 7440 = 2^{4} \times 3 \times 5 \times 31 \]7440 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 40 |
| Sum of divisors | 23808 |
| Euler totient φ(n) | 1920 |
| Square | 55353600 |
| Cube | 411830784000 |
| Square root | 86.255435 (= 4√465) |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 39 |
| Scientific notation | 7.44 × |
7440 in other forms
| Form | Value |
|---|---|
| In words | seven thousand four hundred and forty |
| Binary (base 2) | 1110100010000 |
| Octal (base 8) | 16420 |
| Hexadecimal (base 16) | 1D10 |
| Base 3 | 101012120 |
| As time | 7440 seconds = 2 h 4 min 0 s |
Is 7440 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (7440 ÷ 2 = 3720) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (7440 ÷ 3 = 2480) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (7440 ÷ 4 = 1860) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (7440 ÷ 5 = 1488) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (7440 ÷ 6 = 1240) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 (7440 ÷ 8 = 930) | 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 | Yes (7440 ÷ 10 = 744) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (7440 ÷ 12 = 620) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 7440 a prime number?
No. 7440 = × 3 × 5 × 31, so it is divisible by 2.
What are the factors of 7440?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 31, 40, 48, 60, 62, 80, 93, 120, 124, 155, 186, 240, 248, 310, 372, 465, 496, 620, 744, 930, 1240, 1488, 1860, 2480, 3720, 7440.
What is 7440 in binary?
1110100010000 (hexadecimal 1D10, octal 16420).
What is the square root of 7440?
About 86.2554, exactly 4√465.
Is 7440 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 7440?
7440 is a Harshad number: divisible by its digit sum 15.