The number 735
735 is a composite number with 12 divisors. Its prime factorisation is 3 × 5 × . Divisors (12): 1, 3, 5, 7, 15, 21, 35, 49, 105, 147, 245, 735.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 735: a Harshad number: divisible by its digit sum 15.
- 2
735 is composite. Its prime factorisation is
- 3
The divisors add up to 1368; without 735 itself that is 633, so 735 is deficient (633 is less than 735). Euler's totient φ(735) = 336 numbers up to 735 share no factor with it.
- 4
The digits of 735 add up to 15, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 46 steps to reach 1.
LaTeX source of the formulas on this page
\[ 735 = 3 \times 5 \times 7^{2} \]735 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 1368 |
| Euler totient φ(n) | 336 |
| Square | 540225 |
| Cube | 397065375 |
| Square root | 27.110883 (= 7√15) |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 46 |
| Scientific notation | 7.35 × |
735 in other forms
| Form | Value |
|---|---|
| In words | seven hundred and thirty-five |
| Roman numerals | DCCXXXV |
| Binary (base 2) | 1011011111 |
| Octal (base 8) | 1337 |
| Hexadecimal (base 16) | 2DF |
| Base 3 | 1000020 |
| As time | 735 seconds = 12 min 15 s |
Is 735 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 (735 ÷ 3 = 245) | 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 (735 ÷ 5 = 147) | 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 | Yes (735 ÷ 7 = 105) | 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 | No (remainder 6) | 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 9) | 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 735 a prime number?
No. 735 = 3 × 5 × , so it is divisible by 3.
What are the factors of 735?
1, 3, 5, 7, 15, 21, 35, 49, 105, 147, 245, 735.
What is 735 in binary?
1011011111 (hexadecimal 2DF, octal 1337).
What is the square root of 735?
About 27.1109, exactly 7√15.
What is 735 in Roman numerals?
DCCXXXV.
Is 735 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 735?
735 is a Harshad number: divisible by its digit sum 15.