The number 1440
1440 is a composite number with 36 divisors. Its prime factorisation is × × 5. Divisors (36): 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30 … 1440.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1440: a Harshad number: divisible by its digit sum 9.
- 2
1440 is composite. Its prime factorisation is
- 3
The divisors add up to 4914; without 1440 itself that is 3474, so 1440 is abundant (3474 is more than 1440). Euler's totient φ(1440) = 384 numbers up to 1440 share no factor with it.
- 4
The digits of 1440 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 21 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1440 = 2^{5} \times 3^{2} \times 5 \]1440 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 4914 |
| Euler totient φ(n) | 384 |
| Square | 2073600 |
| Cube | 2985984000 |
| Square root | 37.947332 (= 12√10) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 21 |
| Scientific notation | 1.44 × |
1440 in other forms
| Form | Value |
|---|---|
| In words | one thousand four hundred and forty |
| Roman numerals | MCDXL |
| Binary (base 2) | 10110100000 |
| Octal (base 8) | 2640 |
| Hexadecimal (base 16) | 5A0 |
| Base 3 | 1222100 |
| As time | 1440 seconds = 24 min 0 s |
Is 1440 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (1440 ÷ 2 = 720) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (1440 ÷ 3 = 480) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (1440 ÷ 4 = 360) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (1440 ÷ 5 = 288) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (1440 ÷ 6 = 240) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 (1440 ÷ 8 = 180) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (1440 ÷ 9 = 160) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (1440 ÷ 10 = 144) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 10) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (1440 ÷ 12 = 120) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1440 a prime number?
No. 1440 = × × 5, so it is divisible by 2.
What are the factors of 1440?
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 32, 36, 40, 45, 48, 60, 72, 80, 90, 96, 120, 144, 160, 180, 240, 288, 360, 480, 720, 1440.
What is 1440 in binary?
10110100000 (hexadecimal 5A0, octal 2640).
What is the square root of 1440?
About 37.9473, exactly 12√10.
What is 1440 in Roman numerals?
MCDXL.
Is 1440 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 1440?
1440 is a Harshad number: divisible by its digit sum 9.