The number 2124
2124 is a composite number with 18 divisors. Its prime factorisation is × × 59. Divisors (18): 1, 2, 3, 4, 6, 9, 12, 18, 36, 59, 118, 177, 236, 354, 531, 708 … 2124.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 2124: a Harshad number: divisible by its digit sum 9.
- 2
2124 is composite. Its prime factorisation is
- 3
The divisors add up to 5460; without 2124 itself that is 3336, so 2124 is abundant (3336 is more than 2124). Euler's totient φ(2124) = 696 numbers up to 2124 share no factor with it.
- 4
The digits of 2124 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 125 steps to reach 1.
LaTeX source of the formulas on this page
\[ 2124 = 2^{2} \times 3^{2} \times 59 \]2124 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 18 |
| Sum of divisors | 5460 |
| Euler totient φ(n) | 696 |
| Square | 4511376 |
| Cube | 9582162624 |
| Square root | 46.086874 (= 6√59) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 125 |
| Scientific notation | 2.124 × |
2124 in other forms
| Form | Value |
|---|---|
| In words | two thousand one hundred and twenty-four |
| Roman numerals | MMCXXIV |
| Binary (base 2) | 100001001100 |
| Octal (base 8) | 4114 |
| Hexadecimal (base 16) | 84C |
| Base 3 | 2220200 |
| As time | 2124 seconds = 35 min 24 s |
Is 2124 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (2124 ÷ 2 = 1062) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (2124 ÷ 3 = 708) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (2124 ÷ 4 = 531) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 4) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (2124 ÷ 6 = 354) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (2124 ÷ 9 = 236) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 4) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (2124 ÷ 12 = 177) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 2124 a prime number?
No. 2124 = × × 59, so it is divisible by 2.
What are the factors of 2124?
1, 2, 3, 4, 6, 9, 12, 18, 36, 59, 118, 177, 236, 354, 531, 708, 1062, 2124.
What is 2124 in binary?
100001001100 (hexadecimal 84C, octal 4114).
What is the square root of 2124?
About 46.0869, exactly 6√59.
What is 2124 in Roman numerals?
MMCXXIV.
Is 2124 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 2124?
2124 is a Harshad number: divisible by its digit sum 9.