The number 756
756 is a composite number with 24 divisors. Its prime factorisation is × × 7. Divisors (24): 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 27, 28, 36, 42, 54 … 756.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 756: a Harshad number: divisible by its digit sum 18.
- 2
756 is composite. Its prime factorisation is
- 3
The divisors add up to 2240; without 756 itself that is 1484, so 756 is abundant (1484 is more than 756). Euler's totient φ(756) = 216 numbers up to 756 share no factor with it.
- 4
The digits of 756 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 108 steps to reach 1.
LaTeX source of the formulas on this page
\[ 756 = 2^{2} \times 3^{3} \times 7 \]756 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 2240 |
| Euler totient φ(n) | 216 |
| Square | 571536 |
| Cube | 432081216 |
| Square root | 27.495454 (= 6√21) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 108 |
| Scientific notation | 7.56 × |
756 in other forms
| Form | Value |
|---|---|
| In words | seven hundred and fifty-six |
| Roman numerals | DCCLVI |
| Binary (base 2) | 1011110100 |
| Octal (base 8) | 1364 |
| Hexadecimal (base 16) | 2F4 |
| Base 3 | 1001000 |
| As time | 756 seconds = 12 min 36 s |
Is 756 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (756 ÷ 2 = 378) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (756 ÷ 3 = 252) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (756 ÷ 4 = 189) | 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 (756 ÷ 6 = 126) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (756 ÷ 7 = 108) | 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 | Yes (756 ÷ 9 = 84) | 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 8) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (756 ÷ 12 = 63) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 756 a prime number?
No. 756 = × × 7, so it is divisible by 2.
What are the factors of 756?
1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 27, 28, 36, 42, 54, 63, 84, 108, 126, 189, 252, 378, 756.
What is 756 in binary?
1011110100 (hexadecimal 2F4, octal 1364).
What is the square root of 756?
About 27.4955, exactly 6√21.
What is 756 in Roman numerals?
DCCLVI.
Is 756 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 756?
756 is a Harshad number: divisible by its digit sum 18.