The number 1596
1596 is a triangular number: 1 + 2 + … + 56 = 1596. Its prime factorisation is × 3 × 7 × 19. Divisors (24): 1, 2, 3, 4, 6, 7, 12, 14, 19, 21, 28, 38, 42, 57, 76, 84 … 1596.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1596: a triangular number: 1 + 2 + … + 56 = 1596; a Harshad number: divisible by its digit sum 21.
- 2
1596 is composite. Its prime factorisation is
- 3
The divisors add up to 4480; without 1596 itself that is 2884, so 1596 is abundant (2884 is more than 1596). Euler's totient φ(1596) = 432 numbers up to 1596 share no factor with it.
- 4
The digits of 1596 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 122 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1596 = 2^{2} \times 3 \times 7 \times 19 \]1596 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 4480 |
| Euler totient φ(n) | 432 |
| Square | 2547216 |
| Cube | 4065356736 |
| Square root | 39.949969 (= 2√399) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 122 |
| Scientific notation | 1.596 × |
1596 in other forms
| Form | Value |
|---|---|
| In words | one thousand five hundred and ninety-six |
| Roman numerals | MDXCVI |
| Binary (base 2) | 11000111100 |
| Octal (base 8) | 3074 |
| Hexadecimal (base 16) | 63C |
| Base 3 | 2012010 |
| As time | 1596 seconds = 26 min 36 s |
Is 1596 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (1596 ÷ 2 = 798) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (1596 ÷ 3 = 532) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (1596 ÷ 4 = 399) | 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 (1596 ÷ 6 = 266) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (1596 ÷ 7 = 228) | 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 | 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 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (1596 ÷ 12 = 133) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1596 a prime number?
No. 1596 = × 3 × 7 × 19, so it is divisible by 2.
What are the factors of 1596?
1, 2, 3, 4, 6, 7, 12, 14, 19, 21, 28, 38, 42, 57, 76, 84, 114, 133, 228, 266, 399, 532, 798, 1596.
What is 1596 in binary?
11000111100 (hexadecimal 63C, octal 3074).
What is the square root of 1596?
About 39.9500, exactly 2√399.
What is 1596 in Roman numerals?
MDXCVI.
Is 1596 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 1596?
1596 is a triangular number: 1 + 2 + … + 56 = 1596; a Harshad number: divisible by its digit sum 21.