The number 48072
48072 is a composite number with 16 divisors. Its prime factorisation is × 3 × 2003. Divisors (16): 1, 2, 3, 4, 6, 8, 12, 24, 2003, 4006, 6009, 8012, 12018, 16024, 24036, 48072.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 48072: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
48072 is composite. Its prime factorisation is
- 3
The divisors add up to 120240; without 48072 itself that is 72168, so 48072 is abundant (72168 is more than 48072). Euler's totient φ(48072) = 16016 numbers up to 48072 share no factor with it.
- 4
The digits of 48072 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 96 steps to reach 1.
LaTeX source of the formulas on this page
\[ 48072 = 2^{3} \times 3 \times 2003 \]48072 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 120240 |
| Euler totient φ(n) | 16016 |
| Square | 2310917184 |
| Cube | 111090410869248 |
| Square root | 219.253278 (= 2√12018) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 96 |
| Scientific notation | 4.8072 × |
48072 in other forms
| Form | Value |
|---|---|
| In words | forty-eight thousand and seventy-two |
| Binary (base 2) | 1011101111001000 |
| Octal (base 8) | 135710 |
| Hexadecimal (base 16) | BBC8 |
| Base 3 | 2102221110 |
| As time | 48072 seconds = 13 h 21 min 12 s |
Is 48072 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (48072 ÷ 2 = 24036) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (48072 ÷ 3 = 16024) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (48072 ÷ 4 = 12018) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 2) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (48072 ÷ 6 = 8012) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 (48072 ÷ 8 = 6009) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 2) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 2) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (48072 ÷ 12 = 4006) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 48072 a prime number?
No. 48072 = × 3 × 2003, so it is divisible by 2.
What are the factors of 48072?
1, 2, 3, 4, 6, 8, 12, 24, 2003, 4006, 6009, 8012, 12018, 16024, 24036, 48072.
What is 48072 in binary?
1011101111001000 (hexadecimal BBC8, octal 135710).
What is the square root of 48072?
About 219.2533, exactly 2√12018.
Is 48072 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 48072?
48072 is a happy number: repeatedly adding the squares of its digits reaches 1.