The number 1624
1624 is a composite number with 16 divisors. Its prime factorisation is × 7 × 29. Divisors (16): 1, 2, 4, 7, 8, 14, 28, 29, 56, 58, 116, 203, 232, 406, 812, 1624.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
1624 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
1624 is composite. Its prime factorisation is
- 3
The divisors add up to 3600; without 1624 itself that is 1976, so 1624 is abundant (1976 is more than 1624). Euler's totient φ(1624) = 672 numbers up to 1624 share no factor with it.
- 4
The digits of 1624 add up to 13, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 42 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1624 = 2^{3} \times 7 \times 29 \]1624 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 3600 |
| Euler totient φ(n) | 672 |
| Square | 2637376 |
| Cube | 4283098624 |
| Square root | 40.298883 (= 2√406) |
| Digit sum / digital root | 13 / 4 |
| Collatz steps to 1 | 42 |
| Scientific notation | 1.624 × |
1624 in other forms
| Form | Value |
|---|---|
| In words | one thousand six hundred and twenty-four |
| Roman numerals | MDCXXIV |
| Binary (base 2) | 11001011000 |
| Octal (base 8) | 3130 |
| Hexadecimal (base 16) | 658 |
| Base 3 | 2020011 |
| As time | 1624 seconds = 27 min 4 s |
Is 1624 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (1624 ÷ 2 = 812) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (1624 ÷ 4 = 406) | 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 | No (remainder 4) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (1624 ÷ 7 = 232) | 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 (1624 ÷ 8 = 203) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 4) | 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 7) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1624 a prime number?
No. 1624 = × 7 × 29, so it is divisible by 2.
What are the factors of 1624?
1, 2, 4, 7, 8, 14, 28, 29, 56, 58, 116, 203, 232, 406, 812, 1624.
What is 1624 in binary?
11001011000 (hexadecimal 658, octal 3130).
What is the square root of 1624?
About 40.2989, exactly 2√406.
What is 1624 in Roman numerals?
MDCXXIV.
Is 1624 divisible by 3?
No. Its digits add up to 13, which is not a multiple of 3.
What is special about the number 1624?
It is a composite number with 16 divisors.