The number 407
407 is an Armstrong number: each digit raised to the power 3 adds up to 407. Its prime factorisation is 11 × 37. Divisors (4): 1, 11, 37, 407.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 407: an Armstrong number: each digit raised to the power 3 adds up to 407; a Harshad number: divisible by its digit sum 11; a semiprime: 11 × 37, the product of two primes.
- 2
407 is composite. Its prime factorisation is
- 3
The divisors add up to 456; without 407 itself that is 49, so 407 is deficient (49 is less than 407). Euler's totient φ(407) = 360 numbers up to 407 share no factor with it.
- 4
The digits of 407 add up to 11, and repeating that until one digit is left gives the digital root 2. The Collatz sequence (halve if even, else 3n+1) takes 40 steps to reach 1.
LaTeX source of the formulas on this page
\[ 407 = 11 \times 37 \]
407 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 4 |
| Sum of divisors | 456 |
| Euler totient φ(n) | 360 |
| Square | 165649 |
| Cube | 67419143 |
| Square root | 20.174241 |
| Digit sum / digital root | 11 / 2 |
| Collatz steps to 1 | 40 |
| Scientific notation | 4.07 × |
407 in other forms
| Form | Value |
|---|---|
| In words | four hundred and seven |
| Roman numerals | CDVII |
| Binary (base 2) | 110010111 |
| Octal (base 8) | 627 |
| Hexadecimal (base 16) | 197 |
| Base 3 | 120002 |
| As time | 407 seconds = 6 min 47 s |
Is 407 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | No (remainder 1) | 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 | No (remainder 3) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 2) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 5) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 1) | 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 7) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 2) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 7) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (407 ÷ 11 = 37) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 11) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 407 a prime number?
No. 407 = 11 × 37, so it is divisible by 11.
What are the factors of 407?
1, 11, 37, 407.
What is 407 in binary?
110010111 (hexadecimal 197, octal 627).
What is the square root of 407?
About 20.1742.
What is 407 in Roman numerals?
CDVII.
Is 407 divisible by 3?
No. Its digits add up to 11, which is not a multiple of 3.
What is special about the number 407?
407 is an Armstrong number: each digit raised to the power 3 adds up to 407; a Harshad number: divisible by its digit sum 11; a semiprime: 11 × 37, the product of two primes.