The number 1407
1407 is a composite number with 8 divisors. Its prime factorisation is 3 × 7 × 67. Divisors (8): 1, 3, 7, 21, 67, 201, 469, 1407.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
1407 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
1407 is composite. Its prime factorisation is
- 3
The divisors add up to 2176; without 1407 itself that is 769, so 1407 is deficient (769 is less than 1407). Euler's totient φ(1407) = 792 numbers up to 1407 share no factor with it.
- 4
The digits of 1407 add up to 12, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 171 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1407 = 3 \times 7 \times 67 \]
1407 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 8 |
| Sum of divisors | 2176 |
| Euler totient φ(n) | 792 |
| Square | 1979649 |
| Cube | 2785366143 |
| Square root | 37.509999 |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 171 |
| Scientific notation | 1.407 × |
1407 in other forms
| Form | Value |
|---|---|
| In words | one thousand four hundred and seven |
| Roman numerals | MCDVII |
| Binary (base 2) | 10101111111 |
| Octal (base 8) | 2577 |
| Hexadecimal (base 16) | 57F |
| Base 3 | 1221010 |
| As time | 1407 seconds = 23 min 27 s |
Is 1407 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 | Yes (1407 ÷ 3 = 469) | 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 3) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (1407 ÷ 7 = 201) | 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 3) | 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 | No (remainder 10) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 3) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1407 a prime number?
No. 1407 = 3 × 7 × 67, so it is divisible by 3.
What are the factors of 1407?
1, 3, 7, 21, 67, 201, 469, 1407.
What is 1407 in binary?
10101111111 (hexadecimal 57F, octal 2577).
What is the square root of 1407?
About 37.5100.
What is 1407 in Roman numerals?
MCDVII.
Is 1407 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 1407?
It is a composite number with 8 divisors.