The number 2016
2016 is a triangular number: 1 + 2 + … + 63 = 2016. Its prime factorisation is × × 7. Divisors (36): 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 32 … 2016.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 2016: a triangular number: 1 + 2 + … + 63 = 2016; a Harshad number: divisible by its digit sum 9.
- 2
2016 is composite. Its prime factorisation is
- 3
The divisors add up to 6552; without 2016 itself that is 4536, so 2016 is abundant (4536 is more than 2016). Euler's totient φ(2016) = 576 numbers up to 2016 share no factor with it.
- 4
The digits of 2016 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 112 steps to reach 1.
LaTeX source of the formulas on this page
\[ 2016 = 2^{5} \times 3^{2} \times 7 \]2016 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 6552 |
| Euler totient φ(n) | 576 |
| Square | 4064256 |
| Cube | 8193540096 |
| Square root | 44.899889 (= 12√14) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 112 |
| Scientific notation | 2.016 × |
2016 in other forms
| Form | Value |
|---|---|
| In words | two thousand and sixteen |
| Roman numerals | MMXVI |
| Binary (base 2) | 11111100000 |
| Octal (base 8) | 3740 |
| Hexadecimal (base 16) | 7E0 |
| Base 3 | 2202200 |
| As time | 2016 seconds = 33 min 36 s |
Is 2016 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (2016 ÷ 2 = 1008) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (2016 ÷ 3 = 672) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (2016 ÷ 4 = 504) | 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 (2016 ÷ 6 = 336) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (2016 ÷ 7 = 288) | 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 (2016 ÷ 8 = 252) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (2016 ÷ 9 = 224) | 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 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (2016 ÷ 12 = 168) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 2016 a prime number?
No. 2016 = × × 7, so it is divisible by 2.
What are the factors of 2016?
1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 32, 36, 42, 48, 56, 63, 72, 84, 96, 112, 126, 144, 168, 224, 252, 288, 336, 504, 672, 1008, 2016.
What is 2016 in binary?
11111100000 (hexadecimal 7E0, octal 3740).
What is the square root of 2016?
About 44.8999, exactly 12√14.
What is 2016 in Roman numerals?
MMXVI.
Is 2016 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 2016?
2016 is a triangular number: 1 + 2 + … + 63 = 2016; a Harshad number: divisible by its digit sum 9.