The number 4400
4400 is a composite number with 30 divisors. Its prime factorisation is × × 11. Divisors (30): 1, 2, 4, 5, 8, 10, 11, 16, 20, 22, 25, 40, 44, 50, 55, 80 … 4400.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 4400: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 8.
- 2
4400 is composite. Its prime factorisation is
- 3
The divisors add up to 11532; without 4400 itself that is 7132, so 4400 is abundant (7132 is more than 4400). Euler's totient φ(4400) = 1600 numbers up to 4400 share no factor with it.
- 4
The digits of 4400 add up to 8, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 95 steps to reach 1.
LaTeX source of the formulas on this page
\[ 4400 = 2^{4} \times 5^{2} \times 11 \]4400 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 30 |
| Sum of divisors | 11532 |
| Euler totient φ(n) | 1600 |
| Square | 19360000 |
| Cube | 85184000000 |
| Square root | 66.332496 (= 20√11) |
| Digit sum / digital root | 8 / 8 |
| Collatz steps to 1 | 95 |
| Scientific notation | 4.4 × |
4400 in other forms
| Form | Value |
|---|---|
| In words | four thousand four hundred |
| Binary (base 2) | 1000100110000 |
| Octal (base 8) | 10460 |
| Hexadecimal (base 16) | 1130 |
| Base 3 | 20000222 |
| As time | 4400 seconds = 1 h 13 min 20 s |
Is 4400 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (4400 ÷ 2 = 2200) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (4400 ÷ 4 = 1100) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (4400 ÷ 5 = 880) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 2) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 (4400 ÷ 8 = 550) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 8) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (4400 ÷ 10 = 440) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (4400 ÷ 11 = 400) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 4400 a prime number?
No. 4400 = × × 11, so it is divisible by 2.
What are the factors of 4400?
1, 2, 4, 5, 8, 10, 11, 16, 20, 22, 25, 40, 44, 50, 55, 80, 88, 100, 110, 176, 200, 220, 275, 400, 440, 550, 880, 1100, 2200, 4400.
What is 4400 in binary?
1000100110000 (hexadecimal 1130, octal 10460).
What is the square root of 4400?
About 66.3325, exactly 20√11.
Is 4400 divisible by 3?
No. Its digits add up to 8, which is not a multiple of 3.
What is special about the number 4400?
4400 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 8.