The number 3735
3735 is a binary palindrome (111010010111). Its prime factorisation is × 5 × 83. Divisors (12): 1, 3, 5, 9, 15, 45, 83, 249, 415, 747, 1245, 3735.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 3735: a binary palindrome (111010010111).
- 2
3735 is composite. Its prime factorisation is
- 3
The divisors add up to 6552; without 3735 itself that is 2817, so 3735 is deficient (2817 is less than 3735). Euler's totient φ(3735) = 1968 numbers up to 3735 share no factor with it.
- 4
The digits of 3735 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 38 steps to reach 1.
LaTeX source of the formulas on this page
\[ 3735 = 3^{2} \times 5 \times 83 \]3735 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 6552 |
| Euler totient φ(n) | 1968 |
| Square | 13950225 |
| Cube | 52104090375 |
| Square root | 61.114646 (= 3√415) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 38 |
| Scientific notation | 3.735 × |
3735 in other forms
| Form | Value |
|---|---|
| In words | three thousand seven hundred and thirty-five |
| Roman numerals | MMMDCCXXXV |
| Binary (base 2) | 111010010111 |
| Octal (base 8) | 7227 |
| Hexadecimal (base 16) | E97 |
| Base 3 | 12010100 |
| As time | 3735 seconds = 1 h 2 min 15 s |
Is 3735 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | No (remainder 1) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (3735 ÷ 3 = 1245) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 3) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (3735 ÷ 5 = 747) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 3) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 7) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (3735 ÷ 9 = 415) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 5) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 3) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 3735 a prime number?
No. 3735 = × 5 × 83, so it is divisible by 3.
What are the factors of 3735?
1, 3, 5, 9, 15, 45, 83, 249, 415, 747, 1245, 3735.
What is 3735 in binary?
111010010111 (hexadecimal E97, octal 7227).
What is the square root of 3735?
About 61.1146, exactly 3√415.
What is 3735 in Roman numerals?
MMMDCCXXXV.
Is 3735 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 3735?
3735 is a binary palindrome (111010010111).