The number 748
748 is a composite number with 12 divisors. Its prime factorisation is × 11 × 17. Divisors (12): 1, 2, 4, 11, 17, 22, 34, 44, 68, 187, 374, 748.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 748: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
748 is composite. Its prime factorisation is
- 3
The divisors add up to 1512; without 748 itself that is 764, so 748 is abundant (764 is more than 748). Euler's totient φ(748) = 320 numbers up to 748 share no factor with it.
- 4
The digits of 748 add up to 19, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 46 steps to reach 1.
LaTeX source of the formulas on this page
\[ 748 = 2^{2} \times 11 \times 17 \]748 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 1512 |
| Euler totient φ(n) | 320 |
| Square | 559504 |
| Cube | 418508992 |
| Square root | 27.349589 (= 2√187) |
| Digit sum / digital root | 19 / 1 |
| Collatz steps to 1 | 46 |
| Scientific notation | 7.48 × |
748 in other forms
| Form | Value |
|---|---|
| In words | seven hundred and forty-eight |
| Roman numerals | DCCXLVIII |
| Binary (base 2) | 1011101100 |
| Octal (base 8) | 1354 |
| Hexadecimal (base 16) | 2EC |
| Base 3 | 1000201 |
| As time | 748 seconds = 12 min 28 s |
Is 748 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (748 ÷ 2 = 374) | 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 (748 ÷ 4 = 187) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 3) | 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 6) | 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 1) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 8) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (748 ÷ 11 = 68) | 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 748 a prime number?
No. 748 = × 11 × 17, so it is divisible by 2.
What are the factors of 748?
1, 2, 4, 11, 17, 22, 34, 44, 68, 187, 374, 748.
What is 748 in binary?
1011101100 (hexadecimal 2EC, octal 1354).
What is the square root of 748?
About 27.3496, exactly 2√187.
What is 748 in Roman numerals?
DCCXLVIII.
Is 748 divisible by 3?
No. Its digits add up to 19, which is not a multiple of 3.
What is special about the number 748?
748 is a happy number: repeatedly adding the squares of its digits reaches 1.