The number 450
450 is a composite number with 18 divisors. Its prime factorisation is 2 × × . Divisors (18): 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150 … 450.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 450: a Harshad number: divisible by its digit sum 9.
- 2
450 is composite. Its prime factorisation is
- 3
The divisors add up to 1209; without 450 itself that is 759, so 450 is abundant (759 is more than 450). Euler's totient φ(450) = 120 numbers up to 450 share no factor with it.
- 4
The digits of 450 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 53 steps to reach 1.
LaTeX source of the formulas on this page
\[ 450 = 2 \times 3^{2} \times 5^{2} \]450 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 18 |
| Sum of divisors | 1209 |
| Euler totient φ(n) | 120 |
| Square | 202500 |
| Cube | 91125000 |
| Square root | 21.213203 (= 15√2) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 53 |
| Scientific notation | 4.5 × |
450 in other forms
| Form | Value |
|---|---|
| In words | four hundred and fifty |
| Roman numerals | CDL |
| Binary (base 2) | 111000010 |
| Octal (base 8) | 702 |
| Hexadecimal (base 16) | 1C2 |
| Base 3 | 121200 |
| As time | 450 seconds = 7 min 30 s |
Is 450 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (450 ÷ 2 = 225) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (450 ÷ 3 = 150) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 2) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (450 ÷ 5 = 90) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (450 ÷ 6 = 75) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 | No (remainder 2) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (450 ÷ 9 = 50) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (450 ÷ 10 = 45) | 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 | No (remainder 6) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 450 a prime number?
No. 450 = 2 × × , so it is divisible by 2.
What are the factors of 450?
1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, 450.
What is 450 in binary?
111000010 (hexadecimal 1C2, octal 702).
What is the square root of 450?
About 21.2132, exactly 15√2.
What is 450 in Roman numerals?
CDL.
Is 450 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 450?
450 is a Harshad number: divisible by its digit sum 9.