The number 1416
1416 is a composite number with 16 divisors. Its prime factorisation is × 3 × 59. Divisors (16): 1, 2, 3, 4, 6, 8, 12, 24, 59, 118, 177, 236, 354, 472, 708, 1416.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1416: a Harshad number: divisible by its digit sum 12.
- 2
1416 is composite. Its prime factorisation is
- 3
The divisors add up to 3600; without 1416 itself that is 2184, so 1416 is abundant (2184 is more than 1416). Euler's totient φ(1416) = 464 numbers up to 1416 share no factor with it.
- 4
The digits of 1416 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 34 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1416 = 2^{3} \times 3 \times 59 \]1416 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 3600 |
| Euler totient φ(n) | 464 |
| Square | 2005056 |
| Cube | 2839159296 |
| Square root | 37.629775 (= 2√354) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 34 |
| Scientific notation | 1.416 × |
1416 in other forms
| Form | Value |
|---|---|
| In words | one thousand four hundred and sixteen |
| Roman numerals | MCDXVI |
| Binary (base 2) | 10110001000 |
| Octal (base 8) | 2610 |
| Hexadecimal (base 16) | 588 |
| Base 3 | 1221110 |
| As time | 1416 seconds = 23 min 36 s |
Is 1416 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (1416 ÷ 2 = 708) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (1416 ÷ 3 = 472) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (1416 ÷ 4 = 354) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 1) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (1416 ÷ 6 = 236) | 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 | Yes (1416 ÷ 8 = 177) | 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 6) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 8) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (1416 ÷ 12 = 118) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1416 a prime number?
No. 1416 = × 3 × 59, so it is divisible by 2.
What are the factors of 1416?
1, 2, 3, 4, 6, 8, 12, 24, 59, 118, 177, 236, 354, 472, 708, 1416.
What is 1416 in binary?
10110001000 (hexadecimal 588, octal 2610).
What is the square root of 1416?
About 37.6298, exactly 2√354.
What is 1416 in Roman numerals?
MCDXVI.
Is 1416 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 1416?
1416 is a Harshad number: divisible by its digit sum 12.