The number 1948
1948 is a composite number with 6 divisors. Its prime factorisation is × 487. Divisors (6): 1, 2, 4, 487, 974, 1948.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
1948 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
1948 is composite. Its prime factorisation is
- 3
The divisors add up to 3416; without 1948 itself that is 1468, so 1948 is deficient (1468 is less than 1948). Euler's totient φ(1948) = 972 numbers up to 1948 share no factor with it.
- 4
The digits of 1948 add up to 22, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 143 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1948 = 2^{2} \times 487 \]1948 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 6 |
| Sum of divisors | 3416 |
| Euler totient φ(n) | 972 |
| Square | 3794704 |
| Cube | 7392083392 |
| Square root | 44.136153 (= 2√487) |
| Digit sum / digital root | 22 / 4 |
| Collatz steps to 1 | 143 |
| Scientific notation | 1.948 × |
1948 in other forms
| Form | Value |
|---|---|
| In words | one thousand nine hundred and forty-eight |
| Roman numerals | MCMXLVIII |
| Binary (base 2) | 11110011100 |
| Octal (base 8) | 3634 |
| Hexadecimal (base 16) | 79C |
| Base 3 | 2200011 |
| As time | 1948 seconds = 32 min 28 s |
Is 1948 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (1948 ÷ 2 = 974) | 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 (1948 ÷ 4 = 487) | 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 2) | 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 4) | 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 | No (remainder 1) | 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 1948 a prime number?
No. 1948 = × 487, so it is divisible by 2.
What are the factors of 1948?
1, 2, 4, 487, 974, 1948.
What is 1948 in binary?
11110011100 (hexadecimal 79C, octal 3634).
What is the square root of 1948?
About 44.1362, exactly 2√487.
What is 1948 in Roman numerals?
MCMXLVIII.
Is 1948 divisible by 3?
No. Its digits add up to 22, which is not a multiple of 3.
What is special about the number 1948?
It is a composite number with 6 divisors.