The number 51948
51948 is a composite number with 48 divisors. Its prime factorisation is × × 13 × 37. Divisors (48): 1, 2, 3, 4, 6, 9, 12, 13, 18, 26, 27, 36, 37, 39, 52, 54 … 51948.
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How to work it out
- 1
What is special about 51948: a Harshad number: divisible by its digit sum 27.
- 2
51948 is composite. Its prime factorisation is
- 3
The divisors add up to 148960; without 51948 itself that is 97012, so 51948 is abundant (97012 is more than 51948). Euler's totient φ(51948) = 15552 numbers up to 51948 share no factor with it.
- 4
The digits of 51948 add up to 27, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 202 steps to reach 1.
LaTeX source of the formulas on this page
\[ 51948 = 2^{2} \times 3^{3} \times 13 \times 37 \]51948 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 148960 |
| Euler totient φ(n) | 15552 |
| Square | 2698594704 |
| Cube | 140186597683392 |
| Square root | 227.921039 (= 6√1443) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 202 |
| Scientific notation | 5.1948 × |
51948 in other forms
| Form | Value |
|---|---|
| In words | fifty-one thousand nine hundred and forty-eight |
| Binary (base 2) | 1100101011101100 |
| Octal (base 8) | 145354 |
| Hexadecimal (base 16) | CAEC |
| Base 3 | 2122021000 |
| As time | 51948 seconds = 14 h 25 min 48 s |
Is 51948 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (51948 ÷ 2 = 25974) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (51948 ÷ 3 = 17316) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (51948 ÷ 4 = 12987) | 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 | Yes (51948 ÷ 6 = 8658) | 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 | No (remainder 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (51948 ÷ 9 = 5772) | 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 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (51948 ÷ 12 = 4329) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 51948 a prime number?
No. 51948 = × × 13 × 37, so it is divisible by 2.
What are the factors of 51948?
1, 2, 3, 4, 6, 9, 12, 13, 18, 26, 27, 36, 37, 39, 52, 54, 74, 78, 108, 111, 117, 148, 156, 222, 234, 333, 351, 444, 468, 481, 666, 702, 962, 999, 1332, 1404, 1443, 1924, 1998, 2886, 3996, 4329, 5772, 8658, 12987, 17316, 25974, 51948.
What is 51948 in binary?
1100101011101100 (hexadecimal CAEC, octal 145354).
What is the square root of 51948?
About 227.9210, exactly 6√1443.
Is 51948 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 51948?
51948 is a Harshad number: divisible by its digit sum 27.