The number 48416
48416 is a composite number with 24 divisors. Its prime factorisation is × 17 × 89. Divisors (24): 1, 2, 4, 8, 16, 17, 32, 34, 68, 89, 136, 178, 272, 356, 544, 712 … 48416.
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How to work it out
- 1
What is special about 48416: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
48416 is composite. Its prime factorisation is
- 3
The divisors add up to 102060; without 48416 itself that is 53644, so 48416 is abundant (53644 is more than 48416). Euler's totient φ(48416) = 22528 numbers up to 48416 share no factor with it.
- 4
The digits of 48416 add up to 23, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 70 steps to reach 1.
LaTeX source of the formulas on this page
\[ 48416 = 2^{5} \times 17 \times 89 \]48416 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 102060 |
| Euler totient φ(n) | 22528 |
| Square | 2344109056 |
| Cube | 113492384055296 |
| Square root | 220.036361 (= 4√3026) |
| Digit sum / digital root | 23 / 5 |
| Collatz steps to 1 | 70 |
| Scientific notation | 4.8416 × |
48416 in other forms
| Form | Value |
|---|---|
| In words | forty-eight thousand four hundred and sixteen |
| Binary (base 2) | 1011110100100000 |
| Octal (base 8) | 136440 |
| Hexadecimal (base 16) | BD20 |
| Base 3 | 2110102012 |
| As time | 48416 seconds = 13 h 26 min 56 s |
Is 48416 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (48416 ÷ 2 = 24208) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (48416 ÷ 4 = 12104) | 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 2) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 (48416 ÷ 8 = 6052) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 5) | 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 5) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 48416 a prime number?
No. 48416 = × 17 × 89, so it is divisible by 2.
What are the factors of 48416?
1, 2, 4, 8, 16, 17, 32, 34, 68, 89, 136, 178, 272, 356, 544, 712, 1424, 1513, 2848, 3026, 6052, 12104, 24208, 48416.
What is 48416 in binary?
1011110100100000 (hexadecimal BD20, octal 136440).
What is the square root of 48416?
About 220.0364, exactly 4√3026.
Is 48416 divisible by 3?
No. Its digits add up to 23, which is not a multiple of 3.
What is special about the number 48416?
48416 is a happy number: repeatedly adding the squares of its digits reaches 1.