The number 736
736 is a composite number with 12 divisors. Its prime factorisation is × 23. Divisors (12): 1, 2, 4, 8, 16, 23, 32, 46, 92, 184, 368, 736.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 736: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 16.
- 2
736 is composite. Its prime factorisation is
- 3
The divisors add up to 1512; without 736 itself that is 776, so 736 is abundant (776 is more than 736). Euler's totient φ(736) = 352 numbers up to 736 share no factor with it.
- 4
The digits of 736 add up to 16, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 20 steps to reach 1.
LaTeX source of the formulas on this page
\[ 736 = 2^{5} \times 23 \]736 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 1512 |
| Euler totient φ(n) | 352 |
| Square | 541696 |
| Cube | 398688256 |
| Square root | 27.129320 (= 4√46) |
| Digit sum / digital root | 16 / 7 |
| Collatz steps to 1 | 20 |
| Scientific notation | 7.36 × |
736 in other forms
| Form | Value |
|---|---|
| In words | seven hundred and thirty-six |
| Roman numerals | DCCXXXVI |
| Binary (base 2) | 1011100000 |
| Octal (base 8) | 1340 |
| Hexadecimal (base 16) | 2E0 |
| Base 3 | 1000021 |
| As time | 736 seconds = 12 min 16 s |
Is 736 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (736 ÷ 2 = 368) | 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 (736 ÷ 4 = 184) | 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 | No (remainder 4) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 1) | 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 (736 ÷ 8 = 92) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 7) | 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 10) | 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 736 a prime number?
No. 736 = × 23, so it is divisible by 2.
What are the factors of 736?
1, 2, 4, 8, 16, 23, 32, 46, 92, 184, 368, 736.
What is 736 in binary?
1011100000 (hexadecimal 2E0, octal 1340).
What is the square root of 736?
About 27.1293, exactly 4√46.
What is 736 in Roman numerals?
DCCXXXVI.
Is 736 divisible by 3?
No. Its digits add up to 16, which is not a multiple of 3.
What is special about the number 736?
736 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 16.